IMMUNOCHEMISTRY 


THE  MACMILLAN  COMPANY 

NEW  YORK   •   BOSTON  •    CHICAGO 
ATLANTA  •    SAN   FRANCISCO 

MACMILLAN  &  CO.,  LIMITED 

LONDON   •   BOMBAY  •    CALCUTTA 
MELBOURNE 

THE  MACMILLAN  CO.  OF  CANADA,  LTD. 

TORONTO 


IMMUNOCHEMISTRY 

THE  APPLICATION  OF  THE  PRINCIPLES  OF 

PHYSICAL  CHEMISTRY  TO  THE  STUDY 

OF  THE  BIOLOGICAL  ANTIBODIES 


BY 

SVANTE  AR'RHENIUS 

^ 


Ntto  go* 

THE  MACMILLAN   COMPANY 
1907 

All  rights  reserved 

~ 


COPYRIGHT,  1907, 
BY  THE  MACMILLAN  COMPANY. 

Set  up  and  electrotyped.    Published  October,  1907. 


Nortoootf 

J.  S.  Cashing  Co.  —  Berwick  &  Smith  Co. 
Norwood,  Mass.,  U.S.A. 


PREFACE 

THE  following  pages  contain  a  summary  of  six  lectures 
on  the  Immunity  Reactions  delivered  at  the  University  of 
California,  in  Berkeley,  California,  during  the  summer 
session  of  1904.  The  object  of  the  lectures  was  to  illus- 
trate the  application  of  the  methods  of  physical  chemistry 
to  the  study  of  the  theory  of  toxins  and  antitoxins.  The 
idea  that  the  reciprocal  action  of  toxin  and  antitoxin  is 
of  the  same  nature  as  a  chemical  reaction  is  nearly  as  old 
as  the  study  of  these  phenomena,  which  was  inaugurated 
by  the  discovery  of  the  diphtheria  antitoxin  by  Behring 
and  Kitasato  in  1890.  The  German  school,  led  by  Ehrlich, 
the  renowned  Director  of  the  Prussian  Serum  Institute  in 
Frankfort-on-the-Main,  has  in  particular  done  much  work 
in  support  of  the  opinion  that  the  interaction  of  toxin  and 
antitoxin  is  of  the  nature  of  a  chemical  reaction ;  whereas 
the  French  school,  led  by  Metschnikoff,  tried  to  show  that 
the  effect  of  an  antitoxin  is  chiefly  of  physiological  order, 
an  antitoxin  was  supposed  to  stimulate  in  some  way  the 
organic  tissues  in  their  struggle  against  the  attack  of  the 
poison.1 

When  Ehrlich  succeeded  in  showing  that  the  agglutinat- 
ing action  of  ricin  upon  red  corpuscles  (erythrocytes)  sus- 
pended in  a  physiological  salt-solution  (0.9%  NaCl)  is 
inhibited  by  the  antibody,  —  the  antiricin,  —  the  notion 
that  a  physiological  effect  is  executed  by  the  antibody  was 

1  The  first  studies  in  this  direction  were  carried  out  by  Buchner  (1893) 
and  Roux  and  Vaillard  (1894).  Cf.  Chapter  II. 


Vi  PREFACE 

abandoned  by  most  scientists.  Although  I  adhere  to  the 
chemical  school,  I  cannot  say  that  the  proof  of  Ehrlich  is 
quite  convincing,  since  the  erythrocytes  may  well  be 
regarded  as  "  living  "  even  after  their  separation  from  the 
blood  of  an  animal.  The  further  fact  stated  by  Ehrlich, 
namely,  that  approximately  the  #-fold  quantity  of  a  toxin 
requires  the  n-fo\d  quantity  of  antitoxin  for  its  neutralisa- 
tion, may  be  regarded  as  a  more  convincing  proof  against 
the  physiological  hypothesis.  The  chemical  hypothesis 
is  now  generally  accepted,  and  has  been  adopted  recently 
by  Bordet,  who  originally  expressed  ideas  similar  to  those 
held  by  Metschnikoff. 

Nevertheless,  many  difficulties  to  the  chemical  hypothe- 
sis remained.  Nothing  was  more  natural,  therefore,  than 
that  the  further  elucidation  of  the  problem  should  be 
sought  through  the  aid  of  the  modern  theories  of  solution. 
To  this  end  Madsen  and  Ehrlich  invited  me  to  join  in  their 
work.  My  work  with  Madsen  in  the  Copenhagen  Insti- 
tute enabled  us  to  fix  upon  a  simple  explanation  of  the 
chief  difficulty  exhibited  by  the  so-called  phenomenon  of 
Ehrlich.  The  Chief  of  the  Frankfort  Institute  was  so 
deeply  interested  in  the  progress  of  these  studies  that  he 
invited  me  to  work  in  his  Institute  on  the  chemical  be- 
haviour of  compound  haemolysis.  In  this  case,  also,  it  was 
determined  that  the  laws  of  equilibrium  found  their  appli- 
cation. It  would  seem,  therefore,  that  the  adherents  of 
the  chemical  hypothesis  should  have  felt  wholly  satisfied 
with  the  results.  However,  one  of  the  strange  incidents 
with  which  the  history  of  science  is  replete  occurred.  In 
our  explanation  of  the  investigated  phenomena,  especially 
regarding  the  diphtheria  toxin,  Madsen  and  I,  in  accord- 
ance with  the  usual  rule  in  the  exact  sciences,  tried  to 
employ  as  few  hypotheses  as  possible,  and  in  this  we  fol- 


PREFACE  vii 

lowed  the  example  of  Bordet.  We  tried  to  show  that  the 
phenomena  observed  might  be  explained  on  the  supposition 
that  diphtheria  toxin  is  a  simple  substance  which  slowly 
decomposes  into  an  innocuous  material  that  still  neutralises 
antitoxin.  In  his  explanation  Ehrlich  had  previously 
assumed  the  presence  in  the  diphtheria  poison  of  a  large 
number  of  poisonous  substances  of  different  strength. 
Now  Ehrlich  did  not  wish  to  yield  this  explanation,  which 
he  regards  as  the  principal  point  in  his  doctrine;  and 
therefore  he  and  his  numerous  pupils  raised  a  number  of 
objections  to  the  treatment  of  this  branch  of  science  in 
accordance  with  the  modern  theories  of  chemistry.  There- 
upon Biltz,  encouraged  by  Ehrlich,  took  up  and  elaborated 
the  old  idea  of  Bordet,  which  had  been  abandoned  by  this 
prominent  savant  in  favour  of  the  chemical  hypothesis, 
and  suggested  that  antitoxin  does  not  react  chemically 
with  toxin,  but  behaves  about  in  the  same  manner  as  a 
dye  when  it  becomes  fixed  in  a  fibre. 

Some  of  these  recent  objections  to  the  ideas  brought 
forward  in  the  lectures  have  been  taken  here  into  consid- 
eration, notwithstanding  that  they  have  appeared  since  the 
lectures  were  delivered.  In  the  same  way,  much  recent 
work,  especially  by  Madsen  and  his  pupils  (in  large  part 
as  yet  unpublished),  bearing  upon  the  velocity  of  reactions, 
has  been  given  consideration  in  the  following  pages.  And 
the  recent  work  of  Hamburger  on  precipitins  has  been 
made  use  of  in  the  final  chapter. 

I  have  given  to  these  lectures  the  title  "  Immuno-chem- 
istry,"  and  wish  with  this  word  to  indicate  that  the  chemical 
reactions  of  the  substances  that  are  produced  by  the  injec- 
tion of  foreign  substances  into  the  blood  of  animals,  i.e.  by 
immunisation,  are  under  discussion  in  these  pages.  From 
this  it  follows  also  that  the  substances  with  which  these 


viii  PREFACE 

products  react,  as  proteins  and  ferments,  are  to  be  here 
considered  with  respect  to  their  chemical  properties.  And 
for  the  purpose  of  a  clarification  of  ideas,  other  substances 
that  behave  in  an  analogous  manner  will  be  given  a  con- 
sideration in  the  discussion. 

It  is  evident  that  the  objection  recently  raised  by  Ehrlich 
and  Sachs  to  this  manner  of  investigation,  namely,  that 
it  does  not  enter  upon  the  mode  by  which  the  living 
body  produces  these  so-called  antibodies,  is  quite  true. 
An  investigation  of  the  chemical  relations  of  toxin  and 
antitoxin  need  not  carry  with  it  an  elucidation  of  the 
synthesis  of  the  antitoxin.  But  I  fancy  that  there  are 
many  who  are  so  deeply  interested  in  the  chemical  be- 
haviour of  these  substances  that  they  will  find  an  investi- 
gation of  this  question  well  worthy  of  study.  And  for 
myself,  furthermore,  I  believe  that  the  physiological  side 
of  the  problem,  alluded  to  by  Ehrlich,  will  not  find  a  satis- 
factory solution  until  the  more  simple  chemical  aspect  is 
elucidated. 

The  chief  purpose  of  theoretical  considerations  is  to 
afford  clear  and  concise  ideas  of  the  observed  facts.  They 
thereby  stimulate  scientific  research  to  a  high  degree.  I 
venture  to  hope  that  the  reader  of  the  following  pages  will 
find  that  the  theoretical  views  advanced  by  myself  in  this 
branch  of  science  have  fulfilled  their  role  in  a  most  satis- 
factory manner  during  the  few  years  that  they  have  been 
employed.  I  am  glad  to  say  that  during  these  few  years 
a  large  experimental  material  has  been  produced,  which 
shows  that  the  chief  lines  pointed  out  by  theory  are  closely 
congruent  with  the  facts ;  and  this  material  has  been  pro- 
duced almost  exclusively  in  order  to  verify  the  said  theo- 
retical considerations.  These  have,  therefore,  already  been 
of  great  scientific  use,  and  yet  this  is  only  a  small  part  of 


PREFACE  ix 

what  may  be  expected.  The  reader  will  have  frequent 
opportunities  to  compare  the  different  scientific  points  of 
view  that  are  connected  with  the  theoretical  views  here 
exposed  with  those  founded  on  other  theoretical  consid- 
erations. 

I  am  deeply  indebted  to  my  friend  Professor  Alonzo 
Engelbert  Taylor  of  Berkeley,  California,  for  his  great 
kindness  in  the  revision  of  the  manuscript  and  for  the  cor- 
rection of  some  errors. 

To  my  many  friends  in  California,  these  lines  will,  I 
hope,  recall  the  pleasant  period  of  time  during  which  I 
had  the  good  fortune  to  live  with  them  in  their  agreeable 
country. 

SVANTE  ARRHENIUS. 

STOCKHOLM,  SWEDEN, 
October,  1906. 


CONTENTS 

CHAPTER  PAGE 

I.  INTRODUCTION i 

II.  REVERSIBILITY  OF  REACTIONS  BETWEEN  ANTIBODIES   .      18 

III.  VELOCITY  OF  REACTION.    HOMOGENEOUS  SYSTEMS      .      37 

IV.  VELOCITY  OF  REACTION.    HETEROGENEOUS  SYSTEMS  .    100 
V.  EQUILIBRIA  IN  ABSORPTION  PROCESSES         .        .        .144 

VI.    NEUTRALISATION  OF  THE  H^EMOLYTIC  PROPERTIES  OF 

BASES  AND  OF  LYSINS  OF  BACTERIAL  ORIGIN  .        .167 

VII.    NEUTRALISATION   OF   DIPHTHERIA-TOXIN,  RICIN,  SA- 

PONIN,  AND  SNAKE-VENOMS 196 

VIII.    THE  COMPOUND  H^MOLYSINS 218 

IX.    THE  PRECIPITINS  AND  THEIR  ANTIBODIES     .        .        .  263 

INDEX  OF  AUTHORS 301 

INDEX  OF  MATTER 305 


LECTURES  ON  THE  GENERAL  PROPERTIES 
OF  IMMUNITY 

CHAPTER   I 
INTRODUCTION 

RECENTLY  the  so-called  antibodies  that  are  produced  in 
animals  after  the  injection  of  certain  more  or  less  poison- 
ous substances  have  acquired  a  very  great  importance,  and 
the  chemical  behaviour  of  these  antibodies  has  been  the 
object  of  a  large  number  of  investigations.  Some  of  these 
have  led  to  the  idea  that  the  reactions  of  these  substances 
are  incomplete  and  follow  the  law  of  Guldberg  and  Waage. 
It  is  of  these  researches,  carried  out  chiefly  by  the  Direc- 
tor of  the  Danish  State  Serum  Institute,  Dr.  Thorwald 
Madsen,  and  myself,  that  I  wish  to  give  a  short  review  in 
the  following  lectures. 

For  only  a  few  poisons  have  the  corresponding  anti- 
bodies been  prepared.  These  poisons  are  termed  toxins. 
They  are  all  of  organic  derivation.  Bashf ord l  and  Bes- 
redka2  have  tried  in  vain  to  prepare  antitoxins  to  solanin 
and  saponin  by  the  injection  of  these  substances  into  rab- 
bits and  guinea-pigs.  And  the  so-called  antimorphine  has 
proved  to  be  a  failure.3  Solanin,  saponin,  and  morphin 

1  Bashford:  "Uber  Blutimmunitat,"  Arch,  intern,  dc  pharmacodynamie  et 
de  therapie,  T.  8.  101  et  9.  451  (1901). 

2  Metschnikoff :  "  L'immunite,"  Paris,  1901,  p.  410. 

8  Morgenroth:  Berl.  klin.    Wochenschrift,  1903,  No.  21. 


2  LECTURES  ON   IMMUNITY 

are  therefore  not  toxins.  On  the  other  hand,  extracts  from 
the  seeds  of  Ricinus  communis  contain  a  toxin  called  ricin, 
against  which  we  possess  an  antitoxin  called  antiricin.  In 
the  same  way  antitoxins  are  known  corresponding  to  abrin 
and  robin,  extracted  from  the  seeds  of  Abrus  prcecatorius 
and  of  Robinia  pseudacacia.  It  is  not  only  against  poisons, 
but  also  against  wholly  or  nearly  inoffensive  bodies,  that 
animals  produce  antibodies.  Furthermore  it  seems  that  if 
we  introduce  nearly  any  type  of  cell  into  the  veins  of  an 
animal,  its  blood  will  contain  after  a  time  an  antibody 
which  destroys  the  particular  variety  of  cell.  Even  after 
the  injection  of  rennet,  the  ferment  of  the  coagulation  of 
milk,  we  obtain  an  antibody  called  antirennet,  which 
hinders  the  coagulative  power  of  rennet.1  It  is  very  diffi- 
cult to  draw  a  distinction  between  enzymes  or  ferments  and 
toxins.  Like  rennet,  many  others  of  these  substances  are 
found  to  yield  antibodies  after  injection  into  the  blood  of 
different  animals.  Thus,  for  instance,  v.  Dungern2  pre- 
pared in  this  way  antibodies  against  proteolytic  enzymes 
from  pathogenic  microbes.  Hildebrand  3  obtained  in  a  simi- 
lar way  an  antibody  against  the  ferment  emulsin.  Gessard  4 
found  it  possible  to  prepare  an  antibody  against  tyrosi- 
nase,  an  oxydase  extracted  from  mushrooms ;  and  Sachs 6 
showed  that  the  serum  from  a  goose  which  had  been  in- 
jected with  pepsin  contained  antipepsin. 

A.  Schutze  prepared  "  antilactase  "  by  injection  of  "lac- 
tase  from   kefir"  into  rabbits  or   hens;   other  antibodies 

1  Morgenroth :    Centralblatt  f.  Bakteriologie,  Abt.  I,  Vols.  26  and  27. 

2  v.  Dungern:    Centralblatt  f.  Bakteriologie,  Thl.  I,  Vol.  24  (1898). 
8  Hildebrand:    Virchovfs  Archiv,  Vol.  131  (1893). 

4  Gessard:  Annales  de  Vinstitut Pasteur,  15.  607  (1901). 
6  H.  Sachs:  Fortschritte  d.  medicin,  20.  425  (1902). 


INTRODUCTION  3 

have  been  prepared  against  cynarase,  fibrin  ferment,  pan- 
creatic ferment,  zymase,  and  urease.1 

It  therefore  seems  to  be  only  a  question  of  time  when 
we  shall  be  able  to  prepare  antibodies  against  ferments 
and  enzymes  in  general. 

An  antibody  to  rennet  is  contained  in  the  so-called 
normal  serum  of  the  horse ;  that  is,  horse  blood  freed  of 
fibrin  by  being  shaken  with  small  solid  bodies  such  as  glass 
beads  or  pieces  of  iron  wire,  and  separated  from  the  red 
blood  corpuscles  by  centrifugation.  (This  was  first  shown 
by  Hammarsten  and  Roden.2)  In  the  same  manner  fresh 
serum  and  even  egg-white  contain  antibodies  against  many 
other  substances,  as  for  instance  against  trypsin  and 
tetanolysin.  By  natural  or  normal  blood  serum  is  meant 
that  obtained  from  fresh  animals  that  have  not  been  inocu- 
lated in  any  manner.  If  before  the  preparation  of  the 
blood  serum  foreign  bodies  have  been  injected  into  the 
veins  of  the  animal,  we  obtain  generally  not  normal  serum 
but  serum  containing  an  antibody,  which  is  "  specific " 
to  the  injected  body  (i.e.  immune-serum). 

In  order  to  render  this  peculiar  subject  clearer  I  will 
give  a  short  review  of  the  mode  in  which  these  antibodies 
appear  in  the  serum  and  how  they  afterwards  disappear 
from  it. 

The  next  curve  shows  the  concentration  of  cholera- 
agglutinin  in  the  blood  of  a  goat,  which  had  some  time 
before  the  experiment  been  immunised  with  cultures  of 
Vibrio  cholera,  so  that  the  concentration  of  agglutinin  in  it 

1  Compare  A.  Schiitze  :   Zeitschr.  f.  Hygiene,  48  (1904). 

2  Roden:     Upsala    L'dkarefdrenings  Forhandlingar,    22.    546    (1887); 
Maly's  Jahresbericht,  17.  160  (1887). 


4  LECTURES  ON  IMMUNITY 

was  at  the  commencement  four  arbitrary  units.  If  we 
inject  a  culture  of  the  bacillus  (e.g.  Vibrio  cholera*)  into  the 
blood  of  a  goat,  it  produces  antibodies  specific  to  just  the 
injected  bacilli.  Amongst  these  antibodies  is  one  called 
agglutinin,  because  it  causes  cholera  bacilli  to  clump 
together  and  sink  to  the  bottom  of  the  liquid  in  which 
they  are  suspended.  We  may  measure  the  concentration 
of  agglutinin  in  a  liquid  by  a  method  to  be  described 
below. 

The  experiments,  the  results  of  which  are  given  in  the 
curve,  were  carried  out  by  Madsen  and  Jorgensen,1  follow- 
ing the  subcutaneous  injection  of  40  c.c.  of  a  culture  of  chol- 
era bacilli  into  a  goat.  From  the  jugular  vein  of  the  goat 
small  amounts  of  blood  were  taken  every  day  and  exam- 
ined as  to  their  content  of  agglutinin.  In  the  first  two 
days  no  increase  in  the  quantity  of  agglutinin  in  the 
blood  serum  was  observed,  but  later  on  it  rose  rapidly 
till  it  reached  a  maximum,  "  acme,"  on  the  eighth  day, 
after  which  it  sank  at  first  rapidly,  then  more  slowly. 

The  continuation  of  the  curve  illustrates  an  experiment 
with  the  same  goat,  in  which  an  injection  of  5  c.c.  of  a 
culture  of  cholera  bacilli  was  made  daily  during  the  whole 
period  of  research.  Here  the  first  period,  in  which  no 
agglutinin  was  produced,  lasted  four  days,  and  the  second 
period,  where  the  agglutinin  increased,  eleven  days. 

Madsen  has  found  that  the  decrease  after  the  maximum 
follows  closely  the  equation  for  the  velocity  of  a  chemical 
reaction : 

1  A.  Jorgensen  and  Thorwald  Madsen :  "The  Fate  of  Typhoid  and  Cholera 
Agglutinins,"  Festskrift  oed indviclscn  af  statens  scrum-institut,'V\,  12,  1902, 
Copenhagen. 


cc-o 

UJ- 


u.0 
05 


oo 


Hit 


Q  — 


8 


INTRODUCTION 


Rate  of  decrease  =  const,  (concentration), 
which  gives  the  integrated  formula 


(concentration) 


—  =  const.!  +  const.2  /, 


where  t  represents  the  time  (after  the  maximum)  that  cor- 
responds to  the  concentration  in  the  formula. 

For  the  case  with  cholera  agglutinin  produced  by  goats, 
Madsen  found  n  =  3.5,  const.j  =  0.082  and  0.32  resp.,  and 
const.2  =  o.i3  and  0.032  resp.  for  the  first  and  the  second 
part  of  the  curve  represented  above. 

As  example  we  give  the  figures  of  the  second  part, 
together  with  the  results  of  the  calculation. 


T  (DAYS) 

C°NC-OBS. 

CONC'CALC. 

T  (DAYS) 

C°NC-OB3. 

C°NC-CALC. 

0 

250 

250 

8 

43 

43 

I 

91 

96 

IO 

40 

40 

2 

77 

74 

12 

38 

37 

3 

63 

63 

14 

36 

35 

4 

56 

57 

16 

34 

33 

5 

52 

52 

18 

32 

3i 

6 

49 

48 

20 

30 

3° 

7 

46 

45 

22 

28 

29 

In  this  case  the  exponent  n  was  rather  high,  higher  than 
in  other  cases  examined  by  Madsen.1  For  goats  with 
typhoid  agglutinin  he  found  n  =  1.3  and  #=1.5.  This 
last  figure  was  also  found  for  typhoid  agglutinin  in  the 
blood  of  rabbits.  The  figures  of  Bomstein  for  the  quan- 
tity of  diphtheria-antitoxin  in  the  blood  of  dogs  and  guinea- 

1  Th.  Madsen :  "  The  Decrease  of  Antibodies  in  the  Organism,"  Festskrift, 
VIII,  Copenhagen,  1902. 


LECTURES  ON   IMMUNITY 


pigs  after  direct  injection l  of  this  antibody  in  the  blood  of 
these  animals  gave  #=1.2.  In  this  case  the  constant 
const.2  is  nearly  of  the  same  magnitude  for  different  dogs, 
as  one  might  expect  (it  is  in  three  cases  0.15,  0.18,  and 
0.19).  For  the  destruction  of  antibodies  in  the  human 
body,  Madsen  has  found  n  =  2  in  many  cases.  Of  course 
this  formula  is  only  an  empirical  one.  Its  physical  mean- 
ing is  easily  understood.  The  examples  calculated  by 
Madsen  show  a  very  good  agreement  with  the  experiment. 
As  further  instances  may  be  cited  the  following  figures 
for  the  decomposition  of  typhoid  agglutinin  in  the  blood 
of  a  passively  immunised  goat  (according  to  Jorgensen 
and  Madsen)  and  in  that  pf  a  man  who  had  suffered  from 
typhoid  fever  (according  to  Jorgensen).2  x  =  concentration. 


DESTRUCTION  OF  TYPHOID  AGGLTJTININ  IN  A 

DESTRUCTION  OF  TYPHOID  AGGLUTININ  IN  THE 

PASSIVELY  IMMUNISED  GOAT 

BLOOD  OF  A  MAN  AFTER  TYPHOID  FEVER 

T  (Days) 

'°4x©obs. 

Io4x(l)calc. 

T  (Days) 

<°Oob, 

Io3x©calc. 

0 

II 

II 

0 

17 

17 

0-3 

18 

19 

2 

20 

2O 

I 

30 

3° 

6 

28 

28 

3 

48 

5° 

10 

40 

37 

5 

60 

64 

15 

60 

53 

8 

80 

81 

20 

85 

74 

n 

100 

94 

27 

IOO 

"3 

15 

no 

no 

35 

15° 

1  68 

42 

250 

255 

=  8  X  io-6. 


n  =  1.2. 


const.  2  =  0.0302. 


1  So-called  passive  immunisation:    "Active  immunisation  "  is  produced  by 
injection  of  the  toxins  or  cells  themselves,  as  is  described  above. 

2  Madsen :  "  Lecture  Held  at  the  Meeting  of  Brit.  Med.  Ass.,  Oxford,  July, 
1904,"  British  Medical  Journal,  Sept.  io,  1904. 


INTRODUCTION  7 

The  use  of  formulae  represents  a  great  step  forwards  in 
the  study  of  this  portion  of  the  science  of  immunisation. 
Formerly  investigators  were  content  to  state  that  the 
quantity  of  antitoxin  in  the  blood  decreases  gradually, 
and  in  the  first  stages  more  rapidly  than  later  on.  The 
application  of  the  formula  of  Madsen  teaches  us  much 
more.  It  shows  that  the  phenomenon  is  a  regular  one,  and 
we  are  impelled  to  seek  for  a  cause  for  the  differences  of 
the  values  of  the  constants  n  and  const2.  For  instance,  the 
different  values  of  const.2  for  the  three  days  in  the  experi- 
ments of  Bomstein  —  are  they  really  different  or  do  the 
observed  differences  depend  only  upon  experimental  errors? 
This  and  other  questions  suggest  themselves  after  the  use 
of  such  an  equation,  and  they  lead  to  improvement  in  the 
experimental  methods,  and  to  very  sharp  and  well-defined 
ideas  of  the  natural  phenomena  themselves.  With  the 
help  of  formulas,  which  may  be  empiric  or  rational,  scien- 
tific progress  will  be  much  more  rapid  than  without  them; 
and  as  the  experimental  material  increases,  the  empiric 
formulae  will  probably  be  converted  into  rational  ones,  i.e. 
we  shall  detect  new  laws  of  nature.  It  is  therefore  very 
much  to  be  regretted  that  efforts  have  been  made,  espe- 
cially recently,  to  reject  the  use  of  formulae  in  the  treat- 
ment of  questions  of  serum-therapy.  These  efforts  may 
be  regarded  as  a  last  desperate  struggle  against  the  strin- 
gent conclusions  that  may  be  reached  by  means  of  the 
application  of  mathematical  treatment  —  a  struggle  that 
cannot  be  greatly  prolonged. 

The  injection  of  toxins  or  cells  into  the  blood  of  an  ani- 
mal can  be  done  in  different  ways.  Perhaps  the  most  used 
of  them  is  the  "intravenous  injection"  directly  into  the 


8  LECTURES  ON   IMMUNITY 

veins  of  the  animal ;  as  a  special  case  may  be  regarded  the 
" intracardial  injection"  directly  into  the  heart  of  the  ani- 
mal. More  slowly  acts  the  "  intraperitoneal  injection  "  into 
the  peritoneum,  and  still  more  so  the  "intramuscular  injec- 
tion," or  the  "subcutaneous  injection,"  under  the  skin  of 
the  animal.  This  last  method  is  very  much  used.  In 
these  cases  the  injected  body  reaches  the  blood  very 
slowly,  in  which  fluid  it  produces  antibodies.  The  anti- 
bodies may  be  divided  into  two  great  groups  according  to 
the  nature  of  the  injected  fluid,  whether  it  is  a  homogene- 
ous solution  or  an  emulsion  of  cells,  e.g.  bacteria  or  red 
blood  corpuscles.  These  suspensions  of,  e.g.,  erythrocytes 
are  secured  by  centrifugating  blood  freed  of  fibrin.  Be- 
tween the  centrifugalized  blood  corpuscles  there  still 
remains  a  noticeable  quantity  of  normal  serum.  This 
serum  contains  a  very  effective  reagent  for  most  of  the  re- 
actions which  we  wish  to  study.  It  is  therefore  necessary 
to  wash  it  away.  For  this  purpose  we  use  a  so-called 
physiological  solution,  in  most  cases  of  sodium  chloride 
(0.8-0.9  %)•  Suspended  in  this  solution  blood  corpuscles 
and  most  bacilli  remain  unaltered.  In  stronger  solutions 
the  corpuscles  or  bacilli  contract;  in  weaker  solutions 
the  erythrocytes  give  up  their  red  colouring  matter  and 
remain  colourless  ("  stromata  ").  The  bacilli  are  injured 
by  plasmolysis  or  imbibition  of  water.  To  be  washed,  the 
blood  corpuscles  are  shaken  with  the  physiological  solu- 
tion, centrifugalized,  separated,  and  this  operation  repeated 
until  the  serum  is  washed  away  as  much  as  necessary. 
Usually  two  or  three  washings  with  five  times  the  amount 
of  solution  are  sufficient. 
The  antibodies  produced  after  the  injection  of  a  homo- 


INTRODUCTION  9 

geneous  solution  of  a  substance,  e.g.  a  toxin,  combine  in 
most  cases  with  the  injected  body  to  form  more  innocuous 
compounds.  If  these  compounds  are  soluble  in  the  mix- 
ture, we  call  the  antibodies  antitoxins  (at  least  if  the  injected 
body  is  poisonous).  If,  on  the  contrary,  the  compound  is 
insoluble,  the  antibody  is  called  a  precipitin.  Such  pre- 
cipitins  are  produced  after  the  injection  of  different 
albuminoid  substances. 

If  the  injection  is  a  suspension  of  cells,  the  antibody 
formed  sometimes  dissolves  these  cells ;  in  this  case  it  is 
called  a  lysin.  Thus  after  the  injection  of  bacteria  there 
are  formed  bacteriolysins,  which  under  proper  conditions 
dissolve  the  bacteria  of  the  injected  variety.  After  the 
injection  of  erythrocytes  so-called  haemolysins  are  formed, 
which  produce  haemolysis,  i.e.  cause  the  red  colouring 
matter  (the  haemoglobin)  of  the  injected  erythrocytes  to 
leave  them  and  to  diffuse  into  the  surrounding  liquid. 

In  other  cases,  other  antibodies  are  formed,  often  simul- 
taneously with  lysins,  so-called  agglutinins,  which  produce 
an  agglutination  of  the  injected  cells.  In  this  case  the 
presence  of  salts  plays  an  important  role. 

The  normal  serum  often  contains  a  certain  quantity  of  anti- 
bodies. Thus,  for  instance,  in  the  normal  serum  of  horses  re 
markable  quantities  of  diphtheria-antitoxin  and  of  antirennet 
are  often  found.  This  peculiarity  is  so  frequently  observed, 
that  Ehrlich  supposes  that  all  possible  antibodies  exist  in 
normal  sera,  though  in  most  cases  the  amount  is  not  suffi- 
cient to  be  shown  experimentally.  In  the  blood  of  many 
animals  we  find  two  organic  substances,  cholesterin  and 
lecithin,  which  react  with  many  of  the  injected  poisons  and 
therefore  play  an  important  r61e  as  antitoxins  or  even  as 


IO  LECTURES   ON  IMMUNITY 

constituents  of  toxins.  Thus,  for  example,  the  haemolytic 
poison  tetanolysin  that  is  produced  by  the  Bacillus  tetani 
may  be  interfered  with  in  its  haemolytic  power  by  choles- 
terin.  The  researches  of  Madsen  and  Walbum  seem  to 
prove  that  the  compound  of  these  two  bodies  is  quite  innoc- 
uous, so  that  the  cholesterin  may  be  used  as  an  antibody 
against  tetanolysin.  Now  it  is  not  specific  against  tetanol- 
ysin, as  is  the  antitetanolysin,  but  it  is  effective  also  against 
other  lysins ;  namely,  saponin,  cobralysin,  cobralecithid,  and 
olive  oil,  but  not  against  staphylolysin  and  arachnolysin.1 

The  lecithin,  on  the  other  hand,  combines  with  the 
poison  of  cobra,  so  that  a  haemolysin  cobralecithid  is  formed, 
that  also  in  exceedingly  minute  quantities  exerts  an  haemo- 
lytic influence  upon  erythrocytes.  The  cobra-poison  itself 
displays  such  a  property,  but  to  a  much  less  degree.2 

These  different  bodies  are  often  rather  unstable,  so  that 
they  are  spontaneously  decomposed.  This  decomposition 
proceeds  much  more  rapidly  at  higher  than  at  lower  tem- 
peratures. They  are  therefore  in  most  cases  conserved  at 
very  low  temperatures,  sometimes  in  a  frozen  form. 

Ransom  3  has  made  a  very  interesting  observation  regard- 

1  Kyes  and  Sachs:  Berl.  klin.  Wochenschrift,  1903,  Nos.  2-4. 

2  Overton    has  expressed  the  opinion  that  the  action  of  lecithin  and  of 
cholesterin   are    associated   to   their   lipoidal    properties.      With   respect   to 
lecithin,  it  seems  that  this  idea  may  be  applied  to  much  of  the    experimental 
material.     The  lecithin  seems,  namely,  to  become  dissolved  in  the  membranes 
of  the  cells  (e.g.  the  erythrocytes)  and  thereby  facilitates  the  passage  of  some 
poisonous  substances  (e.g.  mercuric  chloride)  into  the  cell  or  of  haemoglobin 
outwards  through  the  cell  membrane  (cf.  p.  158).      The  action  of  cholesterin 
seems  to  be  quite  different,  and  of  a  neutralizing  character  (cf.  Chap.  VIII). 
On  the  interesting  investigations  of  Overton  regarding  the  permeability  of  cellular 
membranes  cf.  Rud.  Hoeber :  "  Physikalische  Chemie  der  Zelle  und  Gewebe," 
2d  ed.,  Leipzig,  1906,  pp.  163-197. 

3  Deutsche  med,  Wochenschrift,  1901,  No.  13. 


INTRODUCTION  1 1 

ing  the  action  of  cholesterin.  Saponin  is  a  powerful 
haemolytic  agent.  Its  action  is  conditional  upon  the  pres- 
ence of  cholesterin  in  the  blood  corpuscles.  On  the  other 
hand,  cholesterin  in  the  blood  serum  protects  the  blood 
corpuscles  from  being  attacked  by  saponin.  Weigert1 
compared  the  cholesterin  with  a  lightning  conductor,  which 
has  its  proper  place  on  the  outside  of  the  protected  house. 
From  a  chemical  point  of  view  we  explain  the  observation 
in  the  following  manner.  The  membranes  of  the  red 
blood  corpuscles  are  permeable  to  saponin,  but  not  to  cho- 
lesterin or  to  the  haemolytic  compound  of  this  substance 
with  saponin.  Therefore  the  saponin  is  divided  between 
the  blood  corpuscles  and  the  serum  practically  in  propor- 
tion to  their  content  of  cholesterin.  If  the  content  of 
saponin-cholesterm  in  the  blood  corpuscles  reaches  a  certain 
amount,  these  are  haemolysed,  otherwise  not.  It  is  the 
poison  dissolved  in  the  blood  corpuscles  that  exerts  an 
action;  the  poison  on  their  outside  is  without  effect  on 
them. 

The  first  step  in  the  development  of  sero-therapy  into 
an  exact  science  consisted  in  devising  methods  for  measur- 
ing the  quantities  of  the  different  substances  employed. 
In  this  regard  Ehrlich  enjoys  great  distinction  in  having 
been  the  first  who  with  sufficient  exactitude  measured  the 
strength  of  diphtheria-poison.  To  estimate  justly  the 
great  progress  that  was  due  to  the  introduction  of  measure- 
ment methods  by  Ehrlich,  it  must  be  borne  in  mind  that,  at 
the  time  that  Ehrlich  did  his  work,  nearly  all  of  the  leading 
men  believed  it  impossible  to  measure  toxins  and  anti- 

1  C.  Weigert  :  "  Einige  neuere  Arbeiten  zur  Theorie  der  Antitoxinimmuni- 
tat,"  Wiesbaden,  1899. 


12  LECTURES  ON   IMMUNITY 

toxins.  This  belief  was  due  to  the  very  different  effects 
which  the  same  quantity  of  poison  exerted  on  two  different 
individuals  of  the  same  species,  e.g.,  diphtheria-poison  on 
guinea-pigs.  It  was  only  the  practical  necessity  of  having 
measurements  of  the  force  of  poisons  that  led  Ehrlich  to 
overcome  the  great  difficulties.1 

The  chief  investigations  of  Ehrlich  concern  the  diphthe- 
ria-poison and  its  antitoxin.  He  wished  to  determine  the 
lethal  dose  of  this  poison  for  guinea-pigs.  For  this  purpose 
he  injected  a  great  number  of  guinea-pigs  with  different 
doses  ;  they  lay  in  the  neighbourhood  of  the  lethal  doses. 
It  may  be  here  mentioned  that  large  guinea-pigs  in  general 
endure  a  greater  quantity  of  poison  than  do  small  ones. 
Ehrlich  supposed  that  the  resistency  of  different  individ- 
uals was  proportional  to  their  weight,  and  on  this  assump- 
tion he  calculated  the  dose  corresponding  to  a  "  normal " 
guinea-pig  of  250  grammes  weight.  To  obtain  uniform 
results  he  found  it  necessary  to  use  animals  of  nearly  the 
same  weight,  age,  and  race.  In  the  summer  the  animals 
are  more  resistent  and  give  more  uniform  results  than  at 
other  seasons,  when  they  evidently  surfer  from  the  changes 
of  temperature  and  other  climatic  conditions. 

The  lethal  dose  of  diphtheria-toxin  was  defined  by  Ehrlich 
as  the  quantity  which  injected  subcutaneously  into  a  great 
number  of  guinea-pigs  causes  the  death  of  the  larger 
fraction  of  the  animals  in  three  to  four  days,  the  rest  of 
the  animals  dying  about  as  many  before  as  after  this  time. 
According  to  this  method  of  measurement  a  great  deal  of 

JP.  Ehrlich:  "Wertbestimmung  des  Diphtheriheilserums,"  Jena,  1897; 
"Constitution  des  Diphtheriegiftes,"  Deutsche  med.  Wochenschrift,  1898,  No. 
38;  Ehrlich,  Kossel,  and  Wassermann  :  Deutsche  med.  Wochenschrift^  1894. 


INTRODUCTION 


the  material  (namely,  the  animals  killed  in  shorter  or 
longer  times)  is  left  unconsidered.  As  now  the  exactness 
of  the  measurements  increases  sensibly  with  the  material, 
it  is  of  importance  to  use  the  whole  material.  This  may 
be  done  in  the  following  manner.  The  observations  con- 
tain many  cases,  in  which  doses  larger  or  smaller  than  the 
lethal  dose  have  been  injected.  These  observations  offer 
a  statistical  material  of  how  many  days  "  normal "  guinea- 
pigs  live  after  injection  of  1.5,  1.4,  1.3,  1.2,  1.1,0.9,  °-8>  0.7, 
etc.,  lethal  doses.  By  means  of  this  statistical  material  the 
reduction  table  given  below  was  constructed,  by  the  aid  of 
which  all  the  data  regarding  the  killed  guinea-pigs  may 
be  taken  into  consideration.1 


DEATH  AFTER 
DAYS 

INJECTED  LETHAL 
DOSES 

DEATH  AFTER 
DAYS 

INJECTED  LETHAL 
DOSES 

I 

1.6 

5 

0.80 

i«S 

1.4 

6 

0.7I 

2 

1.25 

7 

0.64 

2-5 

I-I5 

8 

0-59 

3 

1.05 

9 

0-55 

3-3 

I.O 

10 

0.51 

3-5 

0.97 

12 

045 

4 

0.91 

H 

0.4 

In  order  to  increase  the  statistical  material,  Madsen 
proposed  to  consider  the  decrease  of  weight  of  the  animals 
in  determining  the  lethal  dose.2  In  this  manner  an  in- 
dependent determination  was  given  for  each  series  of 
measurements. 

1  Arrhenius  and  Madsen :  "  Le  poison  diphterique,"  Oversigt  danskc  Vid- 
sthkforh.,  Copenhagen,  p.  269  (1904). 

2  Arrhenius  and  Madsen :  I.e.,  p.  274. 


14  LECTURES  ON  IMMUNITY 

By  the  aid  of  all  these  different  measurements  it  is 
possible  to  determine  the  probable  error  of  every  measure- 
ment. This  was  omitted  in  all  previous  considerations  of 
this  question.  Under  these  circumstances  an  overestima- 
tion  of  the  exactitude  of  the  measurements  resulted,  which 
often  led  to  conclusions  without  any  solid  foundation. 

The  lethal  dose  of  the  toxin  having  been  determined,  the 
next  step  was  to  standardise  the  solution  of  antitoxin. 
For  this  purpose  Ehrlich  determined  the  quantities  of  the 
solution  in  question  that  were  necessary  to  neutralise  a 
certain  number  (e.g.,  100)  of  lethal  doses  of  the  poison.  As 
experience  has  taught  that  the  antitoxin  is  destroyed 
much  more  slowly  than  the  toxin,  especially  if  it  is  con- 
served with  certain  precautions,  a  given  preparation  of 
diphtheria-antitoxin  is  assumed  as  "  standard  serum,"  and 
the  properties  of  all  poisons  and  antitoxins  to  be  examined 
are  compared  with  this  standard  unit. 

Ehrlich  in  his  measurements  used  the  assumption  that 
injections  of  the  same  quantities  of  free  poison  have  the 
same  effect,  independently  of  the  quantities  of  "neutralized 
poison  "  present.  The  correctness  of  this  assumption  has 
recently  been  subjected  to  question,  to  which  we  will 
return  later. 

The  diphtheria-poison  can  be  measured  as  far  as  we 
know  only  by  the  aid  of  experiments  on  living  animals. 
But  there  are  many  other  poisons  which  may  be  studied 
outside  of  the  living  body,  as  for  instance  the  hasmolysins, 
the  precipitins,  and  the  agglutinins.  Experiments  "in 
vitro "  have  already  long  been  used  in  physiological 
researches,  e.g.  in  digestion,  to  study  processes  outside  of 
the  living  body.  Ehrlich  adopted  this  method  to  study 


INTRODUCTION  15 

the  agglutinating  power  of  ricin  on  erythrocytes  in  the 
presence  of  its  antibody.1  In  this  case  it  is  possible 
to  discriminate  between  different  degrees  of  agglutination 
and  thereby  to  measure  the  quantity  of  free  ricin  present. 
This  method  has  been  developed  chiefly  in  the  Danish 
serum  institute.2 

The  most  fruitful  application  of  these  researches  "in 
vitro  "  has  been  in  the  study  of  the  haemolysins.3  The  lysin 
to  be  investigated  is  added  in  different  quantities  to  circa 
8  c.c.  of  a  suspension  of  2  c.c.  erythrocytes  in  98  c.c.  of 
physiological  salt  solution.  Before  the  admixture  of  lysin, 
water  was  added  to  the  lysin-solution  until  its  total 
quantity  became  10  c.c.  The  best  method  is  to  add  the 
suspension  in  an  energetic  manner  so  that  a  well-mixed 
fluid  immediately  results.  Otherwise  the  lysin  is  con- 
centrated in  some  parts  and  is  absorbed  by  the  erythrocytes 
in  the  proximity,  and  other  erythrocytes  remain  nearly 
intact  if  the  shaking  takes  place  even  a  few  seconds 
(30  to  60)  after  the  mixing.  Therefore  the  usual  result  is 
that  the  haemolysis  is  less  the  longer  the  time  intervening 
between  mixing  and  shaking.  (Variations  of  50  per  cent 
frequently  occur  for  this  reason.)  To  develop  the  haemol- 
ysis, the  test-tubes  are  placed  during  a  certain  time,  gener- 
ally one  or  two  hours,  in  a  water-bath  or  other  thermostat 
at  the  desired  temperature  (in  most  cases  37°  C).  The 
haemolysis  increases  with  time  and  seems  to  tend  to  a 
limit  which  is  reached  the  more  rapidly  the  more  active 

1  Ehrlich :  Fortschritte  der  Medicin,  1897,  No-  2- 

2  Compare  Jorgensen  and  Madsen :  Festskrift,  VI,  6,  Copenhagen,  1902. 

8  Madsen:  "Uber  Tetanolysin,"  Zeitschr.  f.  Hygiene,  32.  p.  214  (1899); 
Arrhenius,  Madsen:  Festskrift,  III,  9,  Copenhagen,  1902. 


!6  LECTURES  ON  IMMUNITY 

the  poison  (at  37°  C.  it  is  reached  in  about  40  minutes  with 
sodium  hydrate,  in  about  100  minutes  with  ammonia,  and 
not  fully  in  200  minutes  with  tetanolysin  as  the  haemolytic 
agent).  After  this  time  the  tubes  are  placed  on  ice  during 
about  twenty-four  hours,  when  the  unattacked  erythrocytes 
fall  to  the  bottom,  leaving  over  them  a  clear  haemoglobin- 
coloured  fluid.  Generally  the  intensity  of  the  colour  is  pro- 
portional to  the  quantity  of  poison  added.  The  strength  of 
the  haemolysis  and  the  colour  proportional  to  it  is  measured 
by  common  colorimetric  methods.  It  is  supposed  that  the 
haemolysis  is  dependent  (under  similar  external  conditions) 
only  on  the  quantity  of  free  lysin  present,  and  not  to  a 
sensible  degree  on  the  quantity  of  bound  lysin  or  antitoxin 
present  in  the  mixture.  By  an  operation  analogous  to 
that  described  under  the  measurement  of  diphtheria-toxin, 
it  is  possible  when  the  haemolysis  lies  between  certain 
limits  (below  total  haemolysis  and  above  a  certain  observ- 
able minimum),  to  use  not  only  a  certain  strength  of  colour, 
but  the  whole  material  of  research,  for  the  comparison. 

The  experiments  "in  vitro"  may  be  carried  out  through 
quite  definite  intervals  of  time  and  at  any  fixed  temperature 
(between  o°  and  1 00°  C. ).  Further,  to  the  fluid  examined,  we 
may  add  large  quantities  of  any  foreign  body  and,  for  in- 
stance, investigate  the  influence  of  different  salts  by  using 
a  physiological  solution  of  cane-sugar  (about  7.2  per  cent) 
for  the  suspension.  It  is  evident  how  much  more  diversified 
knowledge  we  may  obtain  by  these  researches  "  in  vitro  " 
than  by  those  on  living  animals,  which  are  also  expensive, 
and  hence  can  only  be  carried  out  in  a  relatively  small 
number  and  at  the  uncommon  institutions  equipped  with 
well-filled  quarters  for  animals. 


INTRODUCTION  1 7 

The  strengths  of  the  agglutinins  are  measured  by  the 
addition  of  physiological  salt  solution  until  the  mixture  is 
unable  to  produce  a  certain  sharply  observable  agglutina- 
tion of  a  given  suspension  of  cells  in  a  given  time  and  at 
a  definite  temperature.  The  dilution  of  this  mixture  is  a 
measure  of  its  content  of  agglutinin  as  displayed  toward 
the  given  type  of  cells.1  Madsen  and  Jorgensen2  prefer 
to  measure  the  agglutinins  according  to  their  power  of 
clarifying  a  bacterial  suspension. 

Even  for  precipitins  (e.g.  rennet)  such  a  degree  of  pre- 
cipitation or  coagulation  may  be  found  which  is  rather 
sharply  defined  from  higher  or  lower  degrees.  By  inclin- 
ing the  tubes  containing  the  solutions  to  be  investigated 
we  get  an  impression  of  the  consistency  of  the  contents 
after  treatment  during  a  given  time  at  a  definite  tem- 
perature. In  a  similar  way  as  for  the  agglutinins  it  is 
possible  to  determine  the  strength  of  the  precipitating  or 
coagulating  preparations. 

The  bacteriolysins  have  not  been  examined  quantita- 
tively. Their  effects  are  studied  in  mixtures  of  suspensions 
of  bacilli  which  are  injected  intraperitoneally  into  animals 
(e.g.  guinea-pigs)  and  examined  in  specimens  taken  out 
after  a  time.  The  method  of  observation  makes  it  very 
difficult  to  collect  a  material  fit  for  quantitative  treatment. 

1  Eisenbergand  Volk:   Zeitschr.f.  Hygiene,  40.  155  (1902). 

2  Jorgensen  and  Madsen :  Fcstskrift,  I.e. 


COLLEGE    OF    DENTISTRY 
UNIVERSITY  OF  CALIFORNIA 


CHAPTER  II 
REVERSIBILITY  OF  REACTIONS   BETWEEN  ANTIBODIES 

As  has  been  stated,  many  of  the  substances  with  which 
we  deal  in  sero-therapy  are  rather  unstable.  This  insta- 
bility is  very  different  in  different  cases.  Sometimes  (e.g. 
for  snake-venom)  the  toxin  is  more  stable  than  the  anti- 
toxin ;  in  other  cases  (e.g.  for  diphtheria  and  tetanus 
poison)  the  converse  holds  true.  The  snake-venom  resists,  as 
Calmette  showed,  an  elevation  of  the  temperature  to  68°  C., 
which,  however,  destroys  its  antitoxin,  the  antivenin,  in 
aqueous  solution.  This  circumstance  was  used  by  Calmette  l 
to  separate  the  poison  from  the  antivenin;  after  heat- 
ing a  mixture  of  the  two  a  poisonous  solution  remained. 
According  to  more  recent  investigations  of  Martin  and 
Cherry2  this  experiment  is  not  successful  if  the  mixture 
is  held  at  the  temperature  of  the  room  for  more  than  thirty 
minutes  before  the  heating  is  done. 

As  Martin  and  Cherry  intimate,  the  simplest  explanation 
of  this  behaviour  is  that  the  snake-poison  and  the  anti- 
venin require  a  certain  time  to  react  with  each  other. 
Hence  if  the  mixture  is  heated  to  68°  for  ten  minutes  before 
the  reaction  has  practically  reached  the  end-value,  the  free 
antivenin  is  destroyed  and  after  the  heating  the  mixture 
contains  some  free  poison. 

1  Calmette  :    Ann.  de  rinst.  Pasteur,  8.  275  (1894);     Compt.  Rend,  de 
VAc.  de  Sc.  134,  No.  24  (1902). 

2  Martin  and  Cherry  :  Proc.  Roy.  Soc.,  63.  420  (1898). 

18 


REACTIONS  BETWEEN  ANTIBODIES  19 

The  experiments  of  Calmette  yield  therefore  no  evidence 
for  his  conclusion  that  the  binding  of  snake-venom  by 
antivenin  is  a  reversible  process,  whereby  as  soon  as  the 
free  antivenin  is  destroyed,  its  compound  with  the  poison 
is  dissociated  with  the  production  of  new  quantities  of 
poison  and  antivenin.  The  same  comment  may  be  made 
regarding  the  decomposition,  by  boiling,  of  the  innocuous 
mixture  of  a  poison  generated  by  the  Bacillus  pyocyaneus 
and  its  antitoxin.  After  the  boiling,  the  poison,  which  is 
stable  at  that  temperature,  remains  in  the  solution,  while 
the  more  unstable  antitoxin  is  destroyed,  as  Wassermann * 
has  shown. 

But  there  are  many  other  cases  that  demonstrate  rever- 
sible processes  between  analogous  substances  against  which 
no  such  objections  can  be  upheld.  One  of  the  most 
remarkable  of  these  processes  is  used  for  the  production 
of  the  so-called  immune  bodies.  (Ehrlich  terms  them 
"amboceptors.")  If  we  inject  a  suspension  of  the  ery- 
throcytes  of  an  ox  into  the  vein  of  a  rabbit,  this  animal 
after  a  certain  time  presents  in  its  blood  a  hasmolytic 
substance,  which  haemolyses  the  erythrocytes  of  the  blood 
employed;  i.e.  erythrocytes  of  the  ox  and  perhaps  of  some 
nearly  related  species. 

If  we  heat  blood-serum  containing  this  haemolysin  to 
55°  C.  for  about  thirty  minutes,  we  find  that  it  loses  its 
haemolytic  power.  It  is  said  to  be  "inactivated."  The 
hsemolysin  is  evidently  decomposed,  but  a  fraction  of  it 
remains  intact,  as  may  be  shown  by  adding  the  normal 
serum  of  a  guinea-pig.  After  the  addition  of  this  in- 

1  Wassermann  :  Zeitschr.  f.  Hygiene  u.  Infedionskrankhtiten,  22.  263 
(1896). 


20  LECTURES  ON  IMMUNITY 

nocuous  serum,  the  inactivated  serum  has  regained  its 
power  of  haemolysing  bovine  erythrocytes.  (The  guinea- 
pig  serum  has  in  reality  a  slight  haemolytic  action  on 
foreign  erythrocytes,  but  in  the  experiment  it  need  be 
used  in  such  small  dosage  as  to  provoke  in  itself  no  visible 
haemolytic  action.) 

Border.,1  who  discovered  this  interesting  phenomenon, 
concluded  from  his  investigations  that  the  agglutinating 
and  haemolytic  power,  on  erythrocytes  from  a  rabbit,  of 
the  serum  from  a  guinea-pig  which  had  been  treated  with 
five  or  six  injections  of  erythrocytes  (10  c.c.  of  defibrinated 
blood)  of  a  rabbit,  is  due  to  the  presence  of  two  substances, 
of  which  the  one,  the  "immune-body,"  resists  an  elevation 
of  the  temperature  for  thirty  minutes  to  55°  C.,  whereas  the 
other,  the  "alexin"  (Ehrlich's  "complement"),  is  destroyed 
at  that  temperature,  but  may  be  replaced  by  normal  serum 
from  a  guinea-pig  or  even  from  a  rabbit.  Bordet  expressed 
the  opinion  that  the  "  alexin "  serves  as  a  sensibilitator, 
and  renders  the  erythrocytes  susceptible  to  the  "  immune- 
body,"  which  they  are  supposed  not  to  be  in  their  natural 
state. 

Ehrlich,2  on  the  other  hand,  tried  to  demonstrate  that 
the  haemolysin  is  a  compound  of  the  "immune-body"  and 
the  alexin,  which  compound  is  partially  dissociated.  The 
"immune-body"  is  stable  at  higher  temperatures,  the  alexin 
not.  The  alexin  may  be  replaced  by  a  similar  substance, 
an  alexin  contained  in  many  normal  sera.  As  will  be  seen 
in  the  following  pages  (Chapter  VIII),  the  added  alexin  is 
really  consumed  in  the  formation  of  the  haemolysin,  and 

1  Bordet :  Amun.  de  I'Inst.  Pasteur,  12.  692  (1898). 

2  Ehrlich  and  Morgenroth:  Berl.  klin.     Wochenschrift,  No.  I  (1899). 


REACTIONS  BETWEEN  ANTIBODIES  21 

acts  therefore  not  as  a  sensibilitator,  but  is  chemically 
bound,  as  Ehrlich  insists.  This  is  certainly  true  for  the 
alexin  and  " immune-body"  absorbed  by  the  erythrocytes; 
but  the  phenomenon  of  Neisser  and  Wechsberg  indicates 
that  these  two  substances  are  combined  to  a  certain  degree 
even  outside  the  erythrocytes  (compare  Chapter  VIII). 

Here  we  have  evidently  before  us  a  reversible  chemical 
process.  Similar  reversible  processes  are  found  for  all 
the  different  haemolysins  which  are  formed  after  the  in- 
jection of  a  suspension  of  erythrocytes  from  one  animal 
into  the  veins  of  an  animal  of  another  species.  In  a  similar 
manner,  according  to  Ehrlich,  behave  the  bacteriolysins, 
which  are  formed  analogously  to  the  haemolysins.  A 
similar  experiment  was  made  by  Madsen,  Famulener,  and 
Walbum  on  innocuous  mixtures  of  the  haemolytic  agent 
produced  by  staphylococcus,  called  staphylolysin,  and  its 
antitoxin.  Here  the  innocuousness  of  the  mixture  shows 
that  the  haemolysin  is  really  bound,  for  during  the  time  of 
the  reaction,  as  long  as  there  is  some  haemolysin  free,  it  is, 
on  being  mixed  with  a  suspension  of  erythrocytes,  rapidly 
absorbed  by  these,  which  thereafter  lose  their  haemoglobin. 
The  staphylolysin  behaves  in  a  very  peculiar  manner.  If 
it  is  heated  to  70°  C,  it  loses  a  great  deal  of  its  haemolytic 
power,  which,  curiously  enough,  returns  almost  completely 
after  heating  for  five  minutes  to  100°  C.  Its  antitoxin  is 
destroyed  by  such  a  heating.  On  heating  the  innocuous 
mixture  of  staphylolysin  and  its  antitoxin  for  five  minutes 
to  100°  C.,  the  mixture  gains  haemolytic  properties.  The 
binding  of  staphylolysin  with  its  antitoxin  is  therefore  a 
reversible  chemical  process. 

Bordet  injected   the  milk  of  one  animal  into  another 


22  LECTURES  ON  IMMUNITY 

animal  of  another  species  and  found  that  the  serum  from 
this  second  animal  contained  a  substance,  called  lacto- 
serum,  which  gave  a  precipitate  with  the  casein  of  the 
injected  milk.  P.  T.  M tiller,1  who  investigated  the  prop- 
erties of  this  lactoserum,  found  that  it  entered  into  a  com- 
pound with  the  casein  of  the  milk,  which  compound  was 
precipitated  in  the  presence  of  calcium-salts.  Now  the 
lactoserum  is  decomposed  by  heating  to  a  temperature  of 
70  to  71°  for  thirty  minutes.  By  heating  the  precipitate 
which  contained  the  lactoserum  combined  with  casein,  in  a 
solution  of  NaCl,  to  100°  C,  Miiller  succeeded  in  recov- 
ering the  casein  without  loss.  Evidently  the  precipitate 
is  a  little  soluble,  and  the  Dissolved  precipitate  is  partially 
dissociated  into  its  components.  Through  the  high  tem- 
perature the  free  lactoserum  is  destroyed,  then  new 
quantities  of  the  precipitate  are  dissolved,  and  the  process 
goes  on  until  all  the  lactoserum  is  decomposed  and  the 
casein  dissolved  and  recovered. 

There  are  other  methods  of  destroying  one  of  the  com- 
ponents in  an  innocuous  mixture  of  a  toxin  and  its  anti- 
body. Different  chemical  agents  may  destroy  the  one  of 
these  substances  more  rapidly  than  the  other.  Thus  ricin 
is  digested  by  proteolytic  ferment,  but  to  a  much  smaller 
extent  than  its  antibody.  This  behaviour  was  used  by 
Danysz2  for  restoring  the  poisonous  effect  of  ricin  which 
had  been  mixed  with  so  much  antiricin  that  the  resulting 
fluid  was  innocuous.  This  fluid  was  mixed  with  a  solution 
of  ferment  and  left  for  a  sufficient  time  (e.g.  twenty-four 

1  P.  T.  Miiller:  Archiv f.  Hygiene,  44.  150  (1902). 

2  Danysz :  "  Melanges  des  toxines  avec  les  antitoxines,"  Ann.  de  Vlnst.  Pas- 
teur, 16.  311  (1902). 


REACTIONS  BETWEEN  ANTIBODIES  23 

hours)  and  then  found  to  behave  like  a  solution  of  ricin.  In 
this  case  the  process  goes  on  so  slowly  that  the  ricin  and 
antiricin  will  have  had  sufficient  time  to  combine  before 
their  destruction  has  reached  a  noticeable  degree. 

It  is  possible  to  separate  partially  the  two  neutralised  sub- 
stances by  much  less  vigorous  means ;  namely,  by  shaking 
their  solutions  with  other  solvents.  Thus,  for  instance,  Mad- 
sen  and  Noguchi  treated  an  innocuous  mixture  of  saponin 
and  cholesterin,  which  unite  so  rapidly  that  their  velocity 
of  reaction  can  scarcely  be  measured,  in  the  following 
manner.  The  mixture  was  evaporated  to  dryness  and 
thereafter  ground  to  a  powder,  which  was  extracted  with 
chloroform  or  ethyl  ether.  These  fluids  possess  a  great 
dissolving  power  for  cholesterin.  The  residue  of  the 
powder  was  dissolved  in  0.9  per  cent  solution  of  sodium 
chloride.  The  solution  so  prepared  displayed  the  prop- 
erties of  a  solution  of  saponin,  especially  in  regard  to  its 
haemolytic  activity.1 

Another  experiment  of  the  same  nature  was  carried  on 
by  Madsen  and  Walbum.2  They  prepared  a  mixture  of 
ricin  and  antiricin,  which,  after  having  been  exposed  for 
two  hours  to  37°  C.,  showed  no  toxic  effect  when  injected 
into  guinea-pigs.  This  mixture  was  shaken  for  a  time  at 
37°  C.  with  an  equal  quantity  of  a  10  per  cent  suspension  of 
erythrocytes  from  a  rabbit  in  physiological  salt  solution, 
and  then  centrif  ugated.  The  liquid  was  then  shown  to  con- 
tain an  excess  of  antiricin  by  its  attenuation  of  the  aggluti- 

1  Madsen  and  Noguchi :  Oversigt  Ac.  of  Sc.  of  Copenhagen,  No.  6,  p.  461 
(1904). 

'2  Madsen  and  Walbum :  "  De  la  ricine  et  de  1'antitoxin,"  Centralblatt  f. 
Bakteriologie,  36.  253  (1904). 


24  LECTURES  ON   IMMUNITY 

nating  power  of  ricin  on  erythrocytes.  On  the  other  hand, 
the  centrifugated  rabbit-erythrocytes  contained  an  excess 
of  the  nerve  poison  in  ricin;  for  when  they  were  haemolysed 
by  the  addition  of  pure  water  they  gave  a  poisonous  solu- 
tion, which  injected  into  guinea-pigs  produced  death.  In 
this  case  we  have  two  different  poisons, —  the  haemolytic  and 
the  nerve  poison  in  the  ricin  and  the  corresponding  two 
antibodies  in  the  antiricin.  The  experiment  shows  us  that 
both  of  these  poisons  are  bound  to  their  respective  anti- 
bodies by  means  of  reversible  chemical  processes. 

Another  experiment  of  Wassermann  and  Bruck 1  may  be 
explained  in  a  similar  way.  They  injected  an  innocuous 
mixture  of  the  nerve  poison  tetanospasmin  (which  together 
with  the  haemolytic  tetanolysin  is  produced  by  the  Bacillus 
tetani  in  bouillon  medium)  and  its  antitoxin  into  the  hind 
limb  of  a  guinea-pig.  This  animal  showed  no  symptoms 
of  tetanus.  But  if  the  animal  had  previously  received  a 
local  injection  of  adrenalin,  it  was  killed  by  the  injection. 
As  H.  Meyer  and  Ransom  have  shown,  the  antitoxin  is 
chiefly  absorbed  by  the  vascular  system,  the  tetanospasmin 
by  the  nerves.  The  adrenalin  contracts  the  vessels  and 
thus  hinders  the  absorption  of  the  antitoxin,  but  it  has  no 
effect  on  the  nervous  system,  so  that  the  tetanospasmin 
may  execute  its  disastrous  effect.  Hence  the  experiment 
showed  that  the  innocuous  mixture  contained  free  toxin, 
but  we  are  not  quite  certain  in  this  case  that  the  poison 
and  its  antidote  had  had  sufficient  time  to  fully  combine. 

The  simplest  way  to  separate  toxins  from  antitoxins  in 
mixtures  is  by  the  aid  of  diffusion.  Toxins  as  well  as  anti- 
toxins diffuse  in  water  or  in  gel,  but  the  toxins  generally 

1  Wassermann  and  Bruck:  Deutsche  med.  Wochenschrift,  No.  2  (1904). 


REACTIONS  BETWEEN  ANTIBODIES  25 

much  more  rapidly  than  the  antitoxins,  which  are  often  said 
not  to  diffuse.  Madsen  and  I  have  made  an  investigation 
of  this  phenomenon.  In  common  test-tubes  a  5  per  cent 
solution  of  gelatine  was  poured  to  a  height  of  about  10  cm. 
This  solution  solidified  in  a  refrigerator.  After  this  a  solu- 
tion of  toxin  or  antitoxin  was  added  to  a  height  of  1.3  cm. 
above  the  column  of  gel,  and  the  test-tube  placed  on  ice 
(mean  temperature  6°  C.),  where  it  remained  for  sometime, 
(from  one  to  four  or  more  weeks)  according  to  the  diffu- 
sibility  of  the  substance.  After  this  the  fluid  solution  and 
the  different  layers  of  the  column  of  gel  were  analysed  for 
their  content  of  the  different  substances.  By  the  aid  of 
these  determinations  it  is  possible  to  calculate  the  diffusion 
constant  of  the  substances  examined.  In  this  way  we 
found  the  following  constants,  valid  for  12°  C.  and  expressed 
in  days  and  centimeters :  — 

Sodium  chloride 0.94 

Diphtheria-toxin 0.014 

Diphtheria-antitoxin      ....  0.0015 

Tetanolysin 0.037 

Antitetanolysin 0.0021 

To  the  theoretical  meaning  of  these  figures  we  shall 
return  later. 

The  very  slow  diffusion  of  the  other  substances  as  com- 
pared with  that  of  sodium  chloride  is  evidently  connected 
with  their  high  molecular  weight.  This  is  probably  of  the 
same  order  of  magnitude  as  that  found  by  E.  W.  Reid1 

1  E.  W.  Reid :  Journ,  of  Physiology,  33.  13  (1905).  The  molecular  weight 
was  calculated  from  the  osmotic  pressure  of  a  I  per  cent  solution.  This  pres- 
sure was  found  to  be  3.85  mm.  at  15°  C 


26  LECTURES  ON  IMMUNITY 

for  haemoglobin,  viz.  48,000.  For  the  antitoxins  it  may  be 
still  some  ten  or  one  hundred  times  higher. 

As  the  antitoxins  diffuse  about  ten  times  more  slowly 
than  the  toxins,  it  seems  theoretically  possible  to  separate 
them  by  diffusion.  The  first  experiment  in  this  direction 
was  done  by  Martin  and  Cherry.1  They  prepared  60  c.c. 
of  an  innocuous  mixture  of  diphtheria- toxin,  containing 
three  hundred  lethal  doses  and  its  antitoxin,  and  heated  it 
for  two  hours  at  30°  C.  This  mixture  was  allowed  to  filter 
under  pressure  (50  atm.)  through  a  film  of  gelatine  sup- 
ported by  a  Pasteur-Chamberland  filter.  The  filtrate  con- 
tained chiefly  water,  which  passes  through  the  filtrum  very 
much  more  rapidly  than  the  toxin  or  the  antitoxin.  This  fil- 
trate was  examined  and  found  to  contain  per  cubic  centi- 
meter less  than  3  and  5  per  cent  respectively  of  the  poison 
in  one  cubic  centimeter  of  the  original  mixture,  the  poison 
being  supposed  to  be  entirely  free.  Now  water  passes  more 
rapidly  than  sodium  chloride  through  gelatine,  and  sodium 
chloride  about  sixty-seven  times  more  rapidly  than  diph- 
theria-toxin. Hence  we  should  expect  that  even  if  no  poison 
at  all  were  bound,  the  first  filtrate  would  contain  per  cubic 
centimeter  only  1.5  percent  of  the  quantity  of  poison  in  the 
original  mixture.  Later  on  as  the  original  mixture  by  the 
extraction  of  water  became  more  concentrated,  as  seems  to 
have  been  the  case  in  these  experiments,  a  higher  percent- 
age might  have  been  expected.  But  the  conclusion  which 
has  been  drawn  from  them,  that  but  a  small  part,  say  5  per 
cent,  of  the  toxin  was  actually  free,  may  not  be  regarded 
as  warranted  by  the  facts. 

A  similar  experiment  has  been  carried  out  by  Craw  in 

1  Martin  and  Cherry:  Proc.  Roy.  Soc.,  63.  420  (1898). 


REACTIONS  BETWEEN  ANTIBODIES  27 

the  Lister  Institute  on  mixtures  of  a  lysin  from  the  Bacillus 
megatherium  and  its  antitoxin.1  He  found  that  the  poison 
from  innocuous  mixtures  was  concentrated  in  the  gelatin- 
film,  whereas  the  residue  of  the  fluid  exhibited  antitoxic 
properties.  He  therefore  concludes  that  the  binding  of 
this  poison  to  its  antibody  is  due  to  a  "  partially  "  revers- 
ible process.  This  proof  seems  the  more  conclusive,  as 
Craw  evidently  worked  under  theoretical  premises  which 
led  him  to  seek  for  proof  against  the  reversibility  of  the 
process. 

The  experiments  resulted  in  the  same  manner,  even  if  a 
great  excess  of  antilysin,  one  to  three  times  the  "  neutral- 
ising "  quantity,  were  added.  Craw  had  taken  the  precau- 
tion to  heat  his  mixtures  for  three  hours  at  37°  C.  and  then 
to  let  them  stand  one  hour  at  10°  C.,  so  that  there  is  every 
reason  to  believe  that  the  reaction,  which  probably  is  very 
similar  to  that  of  tetanolysin,  had  practically  reached  its 
end.  In  the  filtrate,  Craw  did  not  find  a  trace  of  the 
poison  when  he  worked  with  "  neutral "  or  "  over-neu- 
tralised "  solutions. 

Let  us  for  a  moment  consider  the  ideas  which  led  Craw 
to  suppose  that  the  processes  of  binding  between  toxin 
and  antitoxin  are  not  reversible.  Toxins,  and  specially 
antitoxins,  are  said  to  be  colloids.  Craw  therefore  supposes 
the  so-called  solutions  of  antitoxins  and  the  products  of 
their  reactions  with  toxins  to  be  in  reality  fine  suspensions. 
For  this  statement  no  evidence  is  adduced,  but  it  seems  as 
if  Craw  regarded  the  lack  of  diffusibility  as  characteristic 
of  suspensions,  and  this  may  be  conceded  as  being  correct. 
But  since  Craw  supposes  antitoxins  to  be  non-diffusible,  he 

1  T.  A.  Craw  :   Proc,  Roy.  Soc.t  76.  179  (1905). 


28  LECTURES  ON  IMMUNITY 

seems  not  to  have  known  the  results  of  Madsen's  and  my 
investigations  on  this  point;  instead  he  drew  untenable 
conclusions  from  Brodie's1  experiments,  which  indicate 
that  diphtheria-antitoxin  does  not  in  an  appreciable  degree 
pass  through  a  gelatin  filter  in  a  very  short  time.  We 
may  therefore  leave  the  theoretical  considerations  of  Craw, 
which  he  furthermore  himself  considered  not  to  be  appli- 
cable to  certain  of  his  own  experiments. 

Others  say,  with  Nernst,2  that  the  laws  of  van  't  Hoff 
are  not  applicable  to  colloids,  i.e.  to  toxins  and  antitoxins. 
Nernst  has  himself  shown  that  diffusion  is  caused  by  and 
is  proportional  to  the  osmotic  pressure.  As  now  toxins  and 
antitoxins  diffuse  just  as  other  known  substances,  we  may 
conclude  that  they  obey  van  't  Hoff's  law  of  osmotic  pres- 
sure. In  Madsen's  and  my  experiments  these  substances 
showed  themselves  to  be  distributed  in  the  different  layers 
of  gel  just  as  these  laws  demand.  And  if  van  't  Hoff's 
law  is  found  to  be  valid  for  the  osmotic  pressure  of  these 
substances,  then  also  the  laws  of  chemical  mass-action 
(Guldberg  and  Waage's  law)  must  hold  good  for  their 
reactions.  And  even  if  we  did  not  know  that  these  sub- 
stances behaved  in  this  regard  as  do  other  substances,  we 
would  be  entitled  to  work  with  this  quite  natural  hypothe- 
sis, until  it  was  shown  with  great  accuracy  that  the  hypoth- 
esis was  wrong.  Otherwise  we  would  proceed  in  a 
manner  wholly  different  from  that  used  in  the  other 
disciplines  of  science. 

There  has  been  very  much  discussion  of  this  question 

1  T.  G.  Brodie :  Journ.  of  Pathology  and  Bacteriology,  97.  460-464  (1896). 
3  Nernst  :  "Uber  die  Amvendbarkeit  der  Gesetze  des  chemischen  Gleich- 
gewichts,"  Zeitschr.f.  EUktrochemie,  10,  No.  22  (1904). 


REACTIONS   BETWEEN  ANTIBODIES  2Q 

in  recent  times.  When  Madsen  and  I  calculated  for  the  first 
time  the  action  of  tetanolysin  and  antilysin  upon  each 
other  under  the  supposition  that  this  action  comprehended 
a  reversible  process,  we  knew  also  very  well  that  the  teta- 
nolysin was  simultaneously  subject  to  another  reaction, 
which  destroyed  it  slowly.  But  in  this  circumstance  there 
was  no  reason  for  not  employing  the  known  laws  for  re- 
versible processes.  We  ascertained  for  ourselves  that  the 
influence  of  this  secondary  process  may,  with  the  given 
method  of  experimentation,  be  disregarded.  Had  this  not 
been  the  case,  a  correction  for  the  disturbing  effect  would 
have  been  applied.  Recently  Sachs  1  has  shown  that  an- 
other reaction  than  that  investigated  by  Madsen  and  myself 
takes  place  between  tetanolysin  and  its  antitoxin,  which 
may  to  a  certain  extent  interfere  with  the  chief  reaction 
studied  by  us.  The  simple  relations  found  by  us  seem  to 
indicate  that  in  this  case  also  the  perturbations  caused  by 
the  new  factor  do  not  exceed  a  certain  value,  of  such  a 
magnitude  that  may  be  neglected  in  ordinary  experiments 
on  the  neutralisation  of  tetanolysin.  We  shall  later  on 
return  to  this  question. 

The  incompleteness  of  the  chemical  binding  process 
between  toxins  and  antitoxins  has  aided  in  retarding  the 
idea  that  real  chemical  compounds  are  formed  in  the  union 
of  these  substances.  The  only  chemical  reactions  which 
were  familiar  to  the  scientists  who  studied  the  neutralisa- 
tion of  toxins  were  the  complete  reactions.  Behring,2 
who  was  the  first  in  this  field,  expressed  the  opinion  that 

1  H.  Sachs:  "tiber  die  Constitution  des Tetanolysins," Berl. klin.  Wochen- 
schrift,  No.  16  (1904). 

2  Behring  and  Kitasato  :  Deutsche  med.  Wochcnschrift,  No.  49  (1890). 


30  LECTURES  ON  IMMUNITY 

toxin  is  destroyed  by  antitoxin  without  a  diminution  of  the 
quantity  of  the  latter  substance.  Chemically  speaking,  the 
antitoxin  acted  as  a  catalysator.  This  idea  was  incom- 
patible with  the  measurements  of  Ehrlich  on  diphtheria- 
poison,  according  to  which  the  double  quantity  of  antitoxin 
neutralises  the  double  quantity  of  poison.  Ehrlich  there- 
fore held  the  opinion  that  a  real  chemical  combination 
takes  place.  On  the  other  hand,  Buchner1  and  Roux2 
supposed  that  this  action  of  antitoxin  on  toxin  takes  place 
only  in  the  susceptible  animal.  According  to  their  opinion 
the  antitoxin  really  reacts  upon  the  animal,  stimulating  it 
in  the  struggle  against  the  poison.  This  idea  was  supported 
by  such  experiments  as  those  of  Calmette,  according  to 
which  toxin  and  antitoxin  coexist  in  their  mixtures.  Against 
this  type  of  explanation,  Ehrlich  carried  out  his  experi- 
ments on  the  neutralisation  of  toxins  "in  vitro,"  outside  of 
the  living  animal,  and  Martin  and  Cherry  showed  that  experi- 
ments similar  to  Calmette's  might  be  due  to  an  insufficient 
time  of  reaction.  The  experiments  "in  vitro"  have  been  mul- 
tiplied in  great  number  and  the  influence  of  the  time  of 
reaction  has  been  observed  in  most  cases  investigated,  so 
that  the  idea  of  the  chemical  combination  between  toxins 
and  antitoxins  has  been  generally  accepted.  But  their  in- 
complete knowledge  of  limited  chemical  reactions  caused 
Ehrlich  and  other  investigators  of  these  phenomena  to 
suppose  that  the  processes  observed  are  always  unlimited; 
and  accordingly  they  were  unable  to  explain  all  the  phenom- 
ena indicating  the  existence  of  chemical  equilibria  be- 
tween the  substances  examined.  To  explain  some  of  these 

1  Buchner:  Deutsche  med.  VVochenschrift,  480(1903). 

2  Roux  and  Vaillard:  Ann,  de  rinst.  Pasteur,  8.  724  (1894). 


REACTIONS   BETWEEN  ANTIBODIES  31 

phenomena,  Ehrlich  and  his  school  invented  the  artificial 
hypothesis  that  these  poisons  consist  really  of  a  mixture 
of  a  great  number  of  different  poisonous  and  innocuous 
substances,  which  combine  with  antitoxin.  The  most 
thoroughly  examined  poison,  that  of  diphtheria,  contains, 
according  to  Ehrlich,  not  less  than  eight  such  different 
substances.  Nearly  every  new  phenomenon  led  him  and 
his  school  to  invoke  the  presence  of  a  new  substance. 
Owing  to  this  circumstance  the  theory  of  Ehrlich  has  to  a 
great  degree  lost  its  credibility. 

The  influence  of  the  time  of  reaction  has  also  not  been 
considered  by  Ehrlich  as  much  as  it  should  have  been.  Thus 
for  instance,  Madsen  and  Dreyer1  had  shown  that  a  mix- 
ture of  diphtheria-poison  and  its  antitoxin,  which  is  in- 
nocuous on  subcutaneous  injection  into  guinea-pigs,  kills 
rabbits  on  intravenous  injection-  This  phenomenon  was 
explained  by  Ehrlich2  as  due  to  the  presence  in  the  diph- 
theria-poison of  a  substance  which  could  kill  rabbits  but  not 
guinea-pigs.  The  recent  investigations  of  Morgenroth3 
show  that  the  whole  difference  is  due  to  the  different  modes 
of  injection.  A  mixture  which  is  innocuous  to  guinea-pigs 
when  injected  subcutaneously  may  kill  them  when  injected 
intracardially,  i.e.  directly  into  the  blood.  The  reaction 
between  diphtheria-toxin  and  its  antitoxin  is  not  completed 
in  less  than  a  quarter  of  an  hour,  as  Ehrlich  supposed  from 
his  subcutaneous  injections  into  guinea-pigs;  according  to 
Morgenroth 's  experiments,  this  reaction  requires  several 
hours  at  20°  C.  to  reach  the  equilibrium.  The  experi- 

1  Dreyer  and  Madsen:   Zeitschr.  f.  Hygiene,  37.  250  (1901). 

2  Ehrlich:  Berl.  klin.  Wochenschrift,  Nos.  35-37  (1903). 
8  Morgenroth:  Zeitschr.  f.  Hygiene,  48.  177  (1904). 


32  LECTURES  ON  IMMUNITY 

ments  that  gave  different  results  for  rabbits  and  guinea- 
pigs  were  carried  out  with  nearly  fresh  mixtures  of  poison 
and  antibody.  If  such  a  mixture  be  injected  subcutaneously, 
it  diffuses  into  the  blood  very  slowly  during  several  hours, 
and  in  the  meantime  the  antitoxin  binds  the  toxin.  It  is  not 
necessary,  with  Morgenroth,  to  introduce  a  new  hypoth- 
esis; namely,  that  the  tissues  of  the  guinea-pig  contain 
some  catalytic  agent  reacting  on  the  poison.  The  relatively 
high  temperature  (37°  C.)  of  the  animal  explains  the  rela- 
tively great  velocity  of  the  reaction.  If,  on  the  other  hand, 
the  mixture  is  injected  into  the  veins,  the  poison  is  bound 
by  the  tissues  of  the  animal  before  it  has  time  to  react 
with  the  antitoxin. 

There  are  some  other  processes  common  in  sero-therapy 
which  are  distinguished  by  a  very  high  velocity  of  reaction. 
Thus,  for  instance,  the  agglutinins  react  with  bacteria  in 
less  than  five  minutes  even  at  o°  C.,  according  to  the  experi- 
ments of  Eisenberg  and  Volk.1  (Shorter  times  of  reac- 
tion were  not  examined.)  Here  again  we  observe  a 
reversible  process,  since  the  agglutinin  absorbed  by  the 
bacteria  (or  erythrocytes)  may  be  washed  out  from  them 
with  the  aid  of  a  physiological  salt-solution,  as  Landsteiner 
and  Eisenberg  and  Volk  showed.  It  had  been  supposed 
by  Bordet  that  this  reaction  was  of  the  same  nature  as  the 
adsorption  of  a  dye  by  a  fibre.  But  the  adsorption  phe- 
nomenon is  one  of  slow  velocity ;  the  dyeing  of  fibres  requires 
some  thirty  minutes  at  ioo°C.  and  demands  more  than  two 
days  at  common  room's  temperature  (i7°C).  Therefore 
this  theory  of  Bordet  is  quite  improbable.  I  have  come 
to  the  conclusion  that  the  process  in  question  is  an  absorp- 

1  Eisenberg  and  Volk:   Ztschr.  f.  Hygiene,  40.  155  (1902). 


REACTIONS  BETWEEN  ANTIBODIES  33 

tion  process.  If  we  picture  to  ourselves  bacteria  (or  other 
cells)  of  5  to  10  /*  diameter,  shaken  with  the  solution  of 
a  substance  which  enters  easily  into  the  cells,  we  find  that 
even  if  the  diffusion-constant  of  the  substance  be  so  small 
as  o.ooi,  as  for  the  least  diffusible  antitoxins,  the  process 
of  diffusion  may  reach  its  equilibrium  in  as  short  a  time  as 
less  than  five  minutes. 

We  are  led  to  similar  results  regarding  the  velocity  of 
reaction  by  some  experiments  of  Madsen  and  Walbum. 
They  added  cautiously  a  little  quantity  of  a  solution  of 
tetanolysin  to  10  c.c.  of  a  suspension  of  erythrocytes  in  a 
test-tube,  so  that  the  solution  remained  in  the  uppermost 
layers  of  the  emulsion,  and  shook  the  test-tube  after  the 
lapse  of  thirty  seconds.  In  another  experiment  they  added 
the  suspension  precipitously  to  the  poisonous  solution,  so 
that  the  mixing  took  place  immediately.  The  haemolysis 
in  the  second  experiment  was  nearly  double  that  in  the 
first.  This  is  explained  by  the  fact  that  the  tetanolysin 
has  a  very  much  higher  solubility  in  the  erythrocytes  than 
in  the  surrounding  medium.  During  the  short  time  of  thirty 
seconds  the  uppermost  erythrocytes  had  absorbed  about  30 
per  cent  of  the  poison,  so  that  only  about  70  per  cent  was 
left  for  absorption  by  the  larger  fraction  of  the  erythrocytes. 
In  consequence  of  the  great  absorption-coefficient  of  the 
erythrocytes  these  retain  nearly  the  quantity  of  poison 
which  they  possessed  at  the  moment  of  shaking,  and  the 
final  haemolysis  was  about  as  marked  as  if  only  70  per  cent 
of  the  quantity  of  the  poison  used  had  been  added  in  the 
first  experiment,  supposing  that  it  had  been  distributed 
uniformly  in  the  fluid.  Other  substances  which  are  ab- 
sorbed by  erythrocytes  or  other  cells  seem  to  behave  in 


34  LECTURES  ON  IMMUNITY 

the  same  manner.  In  this  category  belong  the  immune- 
bodies  as  well  as  their  compound  with  alexins,  which,  as 
will  be  seen  later  on,  in  their  absorption  behave  nearly  in 
the  same  manner  as  agglutinins.  Bordet J  showed  that  a 
given  quantity  of  erythrocytes  added  to  a  certain  quantity 
of  blood-haemolysin  gave  a  greater  haemolysis  if  added 
simultaneously,  than  if  it  was  added  in  two  portions,  the 
one  after  the  other. 

That  even  in  this  case  the  process  is  a  reversible  one, 
is  shown  by  an  experiment  of  Morgenroth.2  He  added 
erythrocytes,  which  had  absorbed  immune-body,  to  other 
unprepared  erythrocytes  and  mixed  the  suspension  of  these 
with  alexin.  Not  only  the  originally  prepared  erythrocytes, 
but  also  the  others,  became  haemolysed,  which  shows  that 
a  part  of  the  immune-body  had  left  the  prepared  erythro- 
cytes and  diffused  through  the  surrounding  liquid  to  the 
unprepared  ones.  This  experiment  would  not  succeed  if 
a  sufficient  time  (about  one  hour)  was  not  allotted  to  the 
diffusion  process  before  the  alexin  was  added.  Similar 
experiments  with  analogous  results  were  performed  by 
Joos3  with  typhoid-bacilli  and  their  agglutinin. 

Quite  recently  Morgenroth4  has  done  some  experiments 
with  cobralysin  which  indicate  in  a  very  conclusive  man- 
ner that  this  poison  is  not  destroyed  but  only  bound  by  its 
antitoxin.  He  added  so  much  antitoxin  to  the  cobra- 
poison,  that  its  action  was  wholly  neutralised  and  a  little 
over.  After  seven  days  he  added  to  5  c.c.  of  the  mixture 

1  Bordet :  Ann  de  VInst.  Pasteur,  14.  No.  5  (1900). 
2 Morgenroth:  Munch  med.  Wochenschrift^Q,  2  (1903). 
8  Joos:    Zeitschr.  f.  Hygiene,  40.  203  (1902);   compare  Eisenberg:   Cen- 
tralbl.f.  Bakteriologie,  34.  261,  268  (1903). 

4  Morgenroth:  BerL  klin.  Wochenschrift,  No.  50  (1905). 


REACTIONS  BETWEEN  ANTIBODIES  35 

0.25  c.c.  of  normal  hydrochloric  acid,  which  caused  the 
binding  between  the  toxin  and  antitoxin  to  be  dissolved. 
This  was  proved  by  the  acid  mixture  being  heated  to 
ioo°C.  for  thirty  minutes,  whereby  the  antitoxin  was  de- 
stroyed, whereas  the  poison  itself  was  not  sensibly  weak- 
ened. This  could  be  shown  by  neutralising  the  solution 
after  it  had  cooled  down  to  the  room's  temperature.  The 
toxicity  of  the  solution  was  nearly  the  same  as  that  of 
the  original  solution  without  antitoxin.  In  this  case  the 
peculiarity  occurs,  as  Sachs  has  first  shown,  that  the  pres- 
ence of  acid  protects  the  poison  from  being  destroyed  by 
heat. 

Morgenroth  criticises  a  theory  sketched  by  Nernst1  and 
developed  by  Biltz,  Much,  and  Siebert,2  according  to  which 
the  toxins  are  "adsorbed "to  the  "colloidal"  anti-toxins 
and  thereafter  destroyed.  Morgenroth  says  rightly  that 
this  theory,  "which  as  yet  is  void  of  any  experimental 
basis,"  is  completely  disproved  by  his  experiments. 

As  will  be  shown  later  on,  the  velocity  of  reaction  of 
the  different  toxins  changes  with  temperature  according  to 
a  law  which  was  deduced  from  therm odynamical  considera- 
tions, involving  the  validity  of  van't  Hoff's  law  for  solu- 
tions. The  applicability  of  this  law  to  the  velocities  of 
reaction  of  toxins  may  therefore  be  regarded  as  a  new 
proof  that  the  general  laws  bearing  on  the  behaviour  of 
common  matter  are  valid  even  for  the  processes  going  on 
between  the  substances  studied  in  the  phenomenon  of 
immunity.  No  single  proof  has  been  adduced  against  the 

1  Nernst :  Zeitschr.f.  Elektrochemie,  B.  10,  No.  22  (1904). 

2  Biltz,  Much,  and  Siebert :  Behrings  Beitrage  (1905). 


36  LECTURES  ON   IMMUNITY 

validity  of  these  laws,  and  it  seems  to  me  very  unphilo- 
sophical  a  priori  to  suppose  that  other  laws  should  regulate 
the  reaction  of  toxins  and  antitoxins,  than  those  which 
govern  the  reactions  of  other  substances. 


CHAPTER   III 
VELOCITY  OF  REACTION.    HOMOGENEOUS   SYSTEMS 

WE  have  already  considered  the  velocity  of  the  reaction 
of  the  most  simple  kind  ;  namely,  the  spontaneous  destruc- 
tion of  different  antibodies  in  the  veins  of  animals.  If,  as 
seems  to  be  the  general  case  in  chemistry,  every  molecule 
of  a  substance  is  decomposed  independently  of  all  other 
molecules,  then  the  number  of  molecules  decomposed  dur- 
ing a  short  interval  of  time  is  simply  proportional  to  the 
number  of  molecules  present  at  this  time.  If  this  number 
at  a  certain  time,  which  may  be  regarded  as  the  beginning- 
time  of  the  process,  is  called  A,  and  the  number  of  decom- 

posed molecules  at  a  given  time  t  is  called  x,  then  -—  -  is 

at 

the  rate  of  decrease  of  the  active  molecules,  and  we  get 
the  well-known  equations 


where  t^  corresponds  to  x^  and  /0  to  x§.  Many  such  cases 
are  known  in  chemistry  ;  for  example,  the  decomposition 
of  hydrogen  arsenide  (As  H3).  They  are  called  monomolec- 
ular  reactions.  Monochloracetic  acid  reacts  with  water, 
giving  glycolic  and  hydrochloric  acid,  a  so-called  bimolec- 

37 


38  LECTURES  ON  IMMUNITY 

ular  reaction.      If    now  the  initial  concentration  of   the 
second  group  of  reacting  molecules  is  termed  B,  we  get 


which,  if  B  is  very  large  compared  with  x  and  with  A,  gives 
the  same  solution  as  the  differential  equation  for  the  mono- 
molecular  reaction,  K^  —  KB. 

In  many  cases,  for  instance  in  the  inversion  of  cane 
sugar,  the  one  reacting  molecule  (the  hydrogen  ion)  is 
reformed  by  a  secondary  process  so  rapidly  that  its  con- 
centration may  be  regarded  as  independent  of  the  progress 
of  the  reaction.  In  this  case,  belonging  to  the  so-called 
catalytic  processes,  we  may  also  apply  the  formula  for 
the  monomolecular  reaction,  putting  K  proportional  to  the 
concentration  of  the  unchanged  molecules  (here  the 
//"-ions). 

If  A  =  B,  the  differential  equation  of  the  bimolecular 
reaction  gives  the  solution : 

i  i 


As  a  special  case  may  be  regarded  that  in  which  two  mole- 
cules of  the  same  kind  react  with  each  other. 

If  n  molecules  all  at  the  same  concentration  react  with 
each  other  (the  so-called  ;/-molecular  reaction),  we  find 


which  gives  the  solution  : 

n-l  \n-l 


VELOCITY  OF  REACTION.     HOMOGENEOUS   SYSTEMS       39 

This  equation  was  adopted  by  Madsen  for  the  spontane- 
ous decomposition  of  antibodies,  n  is  in  this  case  no 
whole  number,  and  the  equation  may  be  regarded  as  a 
purely  empirical  rule. 

Very  regular  results  corresponding  to  monomolecular 
reactions  were  found  at  an  investigation  made  by  Madsen 
and  Famulener.  They  studied  the  attenuation  of  vibrio- 
lysin  at  48°  C.  The  haemolytic  power  (/)  of  a  solu- 
tion of  vibriolysin,  held  in  a  thermostat,  was  examined 
at  different  times  (/).  The  power  is  inversely  proportional 
to  the  quantity  of  the  solution  which  is  necessary  to  pro- 
duce a  certain  effect;  e.g.  the  haemolysis  of  10  per  cent  of 
a  2.5  per  cent  suspension  of  erythrocytes  within  an  hour  at 
37°  C.  The  action  evidently  follows  the  law  of  the  mono- 
molecular  reactions,  according  to  the  equation  : 


by  the  aid  of  which  the  calculated  values  /caic.,  which  are  to 
be  compared  with  the  observed  ones  /Obs.>  are  deduced.  The 
temperature  was  46.4°  C.  .£"=0.0079. 


/  (min.) 

4>bs. 

Ajalc. 

O 

1  00.0 

IOO.O 

IO 

78.3 

83.2 

2O 

67.6 

69.5 

30 

59-3 

57-9 

40 

49-8 

48.3 

50 

40.8 

40.4 

60 

344 

33-6 

70 

25.1 

28.1 

80 

23.0 

23-3 

4o 


LECTURES   ON  IMMUNITY 


The  agreement  between  the  observed  and  calculated 
values  is  very  satisfactory,  so  that  there  is  no  doubt  that 
the  law  represented  by  the  differential  equation  deduced 
above  is  really  fulfilled. 

The  influence  of  temperature  on  the  spontaneous  de- 
struction of  vibriolysin  is  very  great,  as  is  shown  by  the 
following  table,  taken  from  a  still  unpublished  work  of 
Madsen  and  Famulener :  — 

RATE  (A*)  OF  DESTRUCTION  OF  VIBRIOLYSIN  AT  DIFFERENT  TEMPERATURES 


TEMP. 

VELOCITY  OF  REACTION 

TEMP. 

VELOCITY 

OBS. 

REACTION 

CALC. 

OBS. 

CALC. 

49-975 
49-75 

0.0778 
0.066 

0.074I' 
0.066 

46.4 
45-97 

0.0079 
0.0063 

0.0081 
0.0062 

49 
48.15 

47-35 

0.039 
0.023 
0.0134 

0.041 
0.024 
0.0128 

45-H5 

0.0057 
0.0036 

0.005  l 
0.0036 

The  calculated  values  are  found  with  help  of  the  formula 


which  has  been  found  to  agree  with  the  experiments  in 
reaction  velocity  in  other  branches  of  physical  chemistry. 
ft  is  128,000,  or  about  five  times  as  great  as  for  the  inversion 
of  cane  sugar  (2 5, 600).  The  velocity  of  reaction  increases 
in  the  proportion  of  10  to  i  in  an  interval  of  3.8  de- 
grees. 

In  a  similar  manner  behaves  tetanolysin,  as  is  seen  from 
the  following  table,  borrowed  from  an  investigation  of 
Madsen  and  Famulener:  — 


VELOCITY  OF  REACTION.     HOMOGENEOUS  SYSTEMS       41 


DECOMPOSITION  OF  TETANOLYSIN 


AT  53.5°  #"!=  0.079 

AT  49.8°  K0  =  0.0047 

t  (min.) 

A>bs. 

/calc. 

t  (min.) 

A>bs. 

/calc. 

0 

1  00.0 

IOO.O 

0 

IOO.O 

IOO.O 

2 

70.9 

69.5 

20 

80.0 

80.6 

4 

43-5 

48.6 

40 

61.1 

64.8 

6 

27.1 

33-6 

60 

52.1 

52.3 

8 

20.4 

23-3 

80 

46.3 

42.1 

10 

14.9 

16.2 

120 

26.8 

26.7 

12 

11.4 

II.  2 

180 

14.6 

14.3 

Here  the  influence  of  temperature  is  still  greater  than  in 
the  decomposition  of  vibrio ly sin ;  /iis  about  162,000.  The 
velocity  of  reaction  corresponds  also  in  this  case  to  that  of 
a  monomolecular  reaction. 

DECOMPOSITION  OF  VIBRIOLYSIN  IN  THE  PRESENCE  OF  0.005  N-  SODIUM 

HYDRATE 


AT  48°  ^=0.0313 


AT   46.5°   A"=  0.012 


/  (min.) 

?obs. 

?calc. 

t  (min.) 

?obs. 

?calc. 

O.O 

IOO.O 

IOO.O 

O 

IOO.O 

IOO.O 

2-5 

83.0 

82.6 

15 

51-7 

48.6 

5-o 

69.4 

69.8 

30 

32.2 

32.2 

7-5 

60.  1 

584 

45 

21.2 

21.2 

1  0.0 

50.0 

48.8 

60 

I4.I 

I4.I 

12.5 

36.5 

40.3 

75 

8.6 

9-3 

150 

32.2 

34.2 

90 

6.2 

6.1 

17-5 

28.2 

28.5 

i°5 

4-4 

4.1 

The  decomposition  of  lysins,  and  generally  speaking  of 
the  substances  dealt  with  in  sero-therapy,  is  increased  to 


42  LECTURES  ON   IMMUNITY 

a  very  high  degree  if  acids  or  bases  are  added  to  their 
solutions.  Madsen  and  Famulener  have,  for  instance, 
investigated  the  rate  of  decomposition  of  a  solution  of 
vibriolysin,  which  contained  so  little  sodium  hydrate  that 
it  was  0.005  n.  in  alkalinity.  They  found  the  above 
figures :  — 

The  constants  of  the  reaction  of  this  monomolecular 
process  are  found  to  be  0.0313  at  48°  and  0.012  at  46.5°  C. 
This  gives  a  value  of  /x  =  128,000,  or  just  the  same  value 
as  that  noted  for  vibriolysin  without  the  addition  of  alkali. 
This  correspondence  may  perhaps  not  be  of  so  great  an 
interest  as  it  seems  at  first,  since  the  solution  of  vibriolysin 
is  in  itself  a  little  alkaline.  .  But  it  is  not  probable  that  its 
alkalinity  is  due  to  sodium  hydrate,  but  chiefly  to  weaker 
organic  bases,  and  therefore  the  coincidence  of  n  in  the 
two  different  cases  is  still  remarkable. 

Other  substances  also  exert  an  influence  upon  the  de- 
struction of  vibriolysin  and  tetanolysin,  although  to  a  much 
less  degree  than  solutions  of  the  alkalies.  Of  these,  am- 
monia has  a  less  influence  than  sodium  hydrate,  but  the  dif- 
ference is  by  far  not  so  accentuated  that  it  would  be  possible 
to  invoke  the  action  of  the  OH  ions.  Thus,  for  instance, 
the  reaction-constant  of  vibriolysin,  which  at  46.2°  reaches 
the  value  0.0066  (per  min.)  is  increased  to  0.081  if  3.4  c.c. 
of  I  n.  NaOH  are  present  in  100  c.c.  of  the  liquid,  and  to 
about  0.075  in  the  presence  of  the  equivalent  quantity  of 
ammonia.  An  addition  of  hydrochloric  acid  gave  different 
results  according  to  its  quantity.  The  first  addition  di- 
minished the  constant  of  reaction,  which  reached  a  mini- 
mum 0.00052  in  the  presence  of  4.25  c.c.  i  n.  HC1  in  100  c.c. 
of  the  liquid.  With  larger  amounts  the  reaction-constant 


VELOCITY   OF   REACTION.     HOMOGENEOUS   SYSTEMS       43 

increased  again,  and  reached  the  value  of  0.022  if  6  c.c., 
and  of  0.109  if  6.75  c.c.  of  i  n.  HC1  was  present  in  100  c.c. 
of  the  liquid.  These  circumstances  seem  to  indicate  that 
some  alkali  present  in  the  original  culture  was  neutralised 
by  the  first  addition  of  the  hydrochloric  acid,  which  there- 
after exerted  its  destructive  action.  The  slight  difference 
between  the  action  of  sodium  hydrate  and  ammonia  leads 
to  the  conclusion  that  the  bases  act  by  setting  some 
alkaline  substance  in  the  bacterial  culture  free.  The  in- 
feriority of  the  ammonia  might  be  explained  by  its  fee- 
bleness, which  allows  an  equilibrium  with  the  base  from 
the  culture  to  be  reached  before  all  the  base  has  been  set 
free. 

Even  the  presence  of  weak  acids,  e.g.  of  acetic  acid, 
accelerates  the  destruction  of  the  vibriolysin.  Thus  9  c.c. 
of  i  n.  CH3  COOH  in  100  c.c.  of  culture  gives  a  reaction- 
constant  0.064,  its  action  corresponding  to  that  of  6.5  c.c. 
i  n.  HC1.  The  weak  acid  exerts  much  less  influence  than 
a  strong  one,  which  was  to  be  expected,  the  neutralised  base 
being  of  less  strength  than  ammonia,  so  that  a  noticeable 
hydrolytic  action  must  occur. 

The  reaction-constant  is,  considering  the  great  errors 
of  observation,  practically  proportional  to  the  amount  of 
base  added  (if  the  alkalinity  exceeds  o.oi  n.);  but 
for  the  action  of  the  acids  no  such  regularity  is  found, 
even  if  we  calculate  from  the  neutralisation  point,  which 
ought  to  nearly  coincide  with  the  point  of  minimal  con- 
stant of  reaction. 

The  content  of  alkali  in  the  natural  solution  of  vibriolysin 
explains  another  fact  found  by  Madsen ;  namely,  that  the 
constant  of  reaction  depends  on  the  initial  concentration 


44  LECTURES  ON  IMMUNITY 

and  is  nearly  proportional  to  it.  In  reality  the  bouillon 
in  which  the  vibrions  grow  is  slightly  alkaline.  Madsen 
found  at  47.8°  C.  that  the  original  solution  of  vibriolysin 
gave  K \  =0.0198.  The  same  solution,  diluted  to  the  con- 
centrations 0.5  or  0.25,  gave  -/T2  =  0.0072  and  ./T4= 0.0039 
respectively.  These  three  figures  are  nearly  in  the  pro- 
portion 4:2:1,  or  as  the  corresponding  concentrations, 
which  is  easily  understood  if  the  alkali  present  exerts  a 
catalytic  influence. 

Much  more  complicated  is  the  influence  which  the  addi- 
tion of  acids  or  of  bases  exerts  upon  the  attenuation  of 
tetanolysin,  which  is  also  in  itself  alkaline.  The  velocity 
of  reaction  K  increases  with  the  amount  of  alkali  added, 
but  decreases  at  first  if  acid  is  added  until  it  reaches  a 
very  flat  minimum,  after  which  it  increases  again  on 
further  addition  of  acid.  This  is  evident  by  an  inspection 
of  the  following  figures  (valid  at  49.83°  C.)  :  — 

98  c.c.  of  tetanolysin  solution  -f     2c.c.  I  n.  NaOH         ^=0.0112 

99  c.c.  of  tetanolysin  solution  +     I  c.c.  I  n.  NaOH  0.0097 
99.5  c.c.  of  tetanolysin  solution  +  0.5  c.c.  I  n.  NaOH  0.0085 

100  c.c.  of  tetanolysin  solution  0.0047 

99  c.c.  of  tetanolysin  solution  +      I  c.c.  I  n.  ^SO*  0.0071 

98  c.c.  of  tetanolysin  solution  +      2  c.c.  I  n.  H2SO*  0.0435 

This  seems  to  indicate  that  the  acid  first  added  is  bound 
by  some  weak  base  in  the  bouillon ;  and  that  the  first 
trace  of  alkali  added  is  also  bound,  probably  in  setting 
some  weak  alkali  free  in  the  bouillon. 

The  figures  for  the  reaction  velocity  in  the  presence  of 
2  c.c.  i  n.  H2SO4  in  looc.c.  are  as  follows,  and  indicate  a 
monomolecular  process:  — 


VELOCITY  OF   REACTION.     HOMOGENEOUS   SYSTEMS       45 


TIME  (min.) 

STRENGTH  (obs.) 

STRENGTH  (calc.) 

O 

100.  0 

97-5 

5 

10 

57-3 
37-7 

59-2 
36.0 

15 

20.  o 

21.7 

20 

14.0 

13-2 

With  regard  to  the  decomposition  of  tetanolysin  in  the 
presence  of  acids  or  bases,  some  experiments  executed  by 
myself  gave  the  following  results  :  — 

On  addition  of  equimolecular  quantities  of  hydrochloric, 
oxalic,  citric,  and  tartaric  acid  (about  0.003  m°l-  normal), 
the  velocity  of  reaction  was  increased  so  much  that  the 
decomposition  of  a  i  per  cent  solution  of  tetanolysin  was 
three-fourths  accomplished  in  ten  minutes.  Of  sulphuric 
acid  half  this  quantity  was  sufficient  for  the  same  purpose, 
and  for  acetic  acid  a  quantity  seventy-five  times  as  great. 
The  said  concentrations  all  contain  nearly  the  same  quan- 
tity of  hydrogen  ions,  and  it  seems,  therefore,  probable 
that  this  catalytic  action  is  caused  by  the  hydrogen  ions. 
Sodium  hydroxide  acts  nearly  as  strongly  as  a  strong  acid 
of  the  same  molecular  concentration ;  but  an  ammonia  so- 
lution of  the  same  concentration  had  a  very  little  influence. 
It  was  necessary  to  use  it  in  about  thirty  times  as  high  a 
concentration  as  sodium  hydrate  to  obtain  the  same  effect. 
Both  these  solutions  have  also  nearly  the  same  concentra- 
tion of  hydroxyl  ions. 

With  the  aid  of  these  experiences,  it  is  very  easy  to  in- 
terpret a  phenomenon  observed  by  Ritchie.1  He  mixed  a 
-solution  of  tetanolysin  with  a  small  quantity  of  hydrochloric 

*  Ritchie:  Jaurn.  of  Hygiene,  1.  130  ( 


46  LECTURES   ON   IMMUNITY 

acid  at  ordinary  room  temperature.  After  a  certain 
time  he  injected  this  mixture  subcutaneously  into  a  guinea- 
pig.  The  animal  was  not  killed  by  the  poison;  but  if 
before  the  injection  the  hydrochloric  acid  was  neutralised 
by  sodium  hydrate,  the  animal  was  killed.  Ritchie  inferred 
that  the  tetanolysin  had  been  destroyed  by  the  hydro- 
chloric acid,  and  was  restored  by  the  addition  of  the  base. 
The  simple  explanation  is  the  following:  The  quantity  of 
acid  added  was  not  sufficient  to  cause  a  rapid  destruction 
of  the  tetanolysin  at  the  low  temperature  of  the  room.  But 
after  the  subcutaneous  injection  the  temperature  of  the 
mixture  rose  rapidly  to  about  37°  C,  and  therefore  corre- 
spondingly the  destruction  of  the  tetanolysin  went  on  with 
great  speed  —  according  to  the  figures  given  above  about 
200,000  times  more  rapidly  than  at  20°  C.  —  before  it  had 
time  to  diffuse  into  the  body  of  the  animal.  Therefore 
the  poison  was  nearly  instantaneously  destroyed,  and  had 
no  sensible  action  on  the  animal.  But  if  before  the  injec- 
tion of  the  mixture  the  acid  was  neutralised  (at  room 
temperature)  by  the  addition  of  an  equivalent  quantity  of 
sodium  hydrate,  then  the  poison  was  not  destroyed  after 
its  injection,  and  could  therefore  exert  its  fatal  influence. 
It  is  not  at  all  necessary  to  assume  such  a  wonderful  pro- 
cess as  a  restoration  of  the  destroyed  toxin-molecules  by 
the  addition  of  the  base. 

For  antitoxins,  very  few  investigations  have  been  car- 
ried through  regarding  their  destruction  in  time.  Madsen 
found  for  antiricin  (serum  of  an  injected  goat)  that  its 
strength  fell  at  room  temperature  to  40  per  cent  in  forty- 
seven  days  and  to  19.6  per  cent  in  eighty-nine  days,  which 
corresponds  rather  closely  to  a  monomolecular  process ; 


VELOCITY  OF   REACTION.     HOMOGENEOUS   SYSTEMS        47 


that  is,  the  rate  of  decrease  of  strength  of  the  solution  was 
proportional  to  the  strength  itself. 

The  greatest  increase  in  the  velocity  of  a  reaction  with 
increase  in  temperature  that  has  ever  been  found  is  that 
of  the  decomposition  of  haemolysin  contained  in  normal 
goat's  serum,  which  dissolves  erythrocytes  from  the  rabbit. 
Madsen  and  Famulener  give  for  this  reaction  the  follow- 
ing figures:  — 

DECOMPOSITION  OF  A  HAEMOLYSIN  AT  53°  AND  5i°C.  (MADSEN  AND  FAMU- 
LENER) 


/  (min.) 

^obs. 

*calc. 

t  (rain.) 

?obs. 

*calc. 

0.0 

100.0 

100.0 

o 

IOO.O 

IOO.O 

2-5 

58.3 

58.2 

5 

74-3 

73.4 

5-o 

44-3 

33-4 

10 

58.3 

62.5 

7-5 

17.9 

19-3 

15 

48.8 

53.3 

20 

44.9 

45-4 

25 

40.0 

38.7 

30 

33-7 

33-° 

35 

28.4 

28.1 

40 

25.2 

24.0 

fji  was  for   this   monomolecular   reaction   found   to   be 
198,500;  with  the  aid  of   this  figure  the  following  table 
is  calculated :  — 
INFLUENCE  OF  THE  TEMPERATURE  ON  THE  DECOMPOSITION  OF  A  H^MOLYSIN 


TEMP. 

VELOCITY  OF  REACTION 

TEMP. 

VELOCITY  OF  REACTION 

OBS. 

CALC. 

OBS. 

CALC. 

53-o 

52.5 
52.0 

0.095 
O.o6o 
0.038 

0.095 
O.O6O 
0.038 

Sl-S 
5I.O 

0.025 
0.0139 

0.024 
0.0145 

Here  we  evidently  observe  two  concomitant  processes. 
Probably  the  process  which  corresponds  to  the  observed 


48 


LECTURES  ON  IMMUNITY 


figures,  is  that  of  the  decomposition  of  haemolysin  into 
immune-body  and  alexin,  and  the  alexin  is  destroyed  still 
more  rapidly.  But  the  reverse  may  also  be  true.  The 
figures  indicate  that  at  60°  C.  a  heating  for  o.i  minute  will 
practically  decompose  the  haemolysin  totally  and  give  a 
solution  of  immune-body  free  from  alexin. 

The  first  reaction  of  enzymes  —  namely,  the  influence 
of  emulsin  on  salicin,  studied  by  Tammann  according  to 
methods  used  in  physical  chemistry —  seems  to  be  of  a 
complicated  nature.  The  process  seems  to  be  monomolec- 
ular  at  low  temperatures,  as  is  shown  by  the  following 
figures,  indicating  the  strength  (concentration)  of  a  solu- 
tion containing  in  the  beginning  3.007  g.  salicin  and  0.08  g. 
emulsin  in  100  c.c. 

DESTRUCTION  OF  SALICIN  BY  EMULSIN  AT  25°  C. 


TIME  (hours) 

STRENGTH  (obs.) 

STRENGTH  (calc.) 

0 

too 

100 

I 

87 

88 

3 

68 

67 

5 

42 

52 

8 

35 

35 

12 

24 

21 

26 

9 

3 

^=0.057. 

The  last  figures  seem  to  indicate  that  the  process  is  re- 
tarded at  its  end.  This  is  still  more  conspicuous  at  higher 
temperatures.  Therefore  we  should  not  overestimate  the 
accuracy  of  p  calculated  from  Tammann's  figures  and 
giving  fi  =  3330,1  corresponding  to  an  increase  in  the 
proportion  of  only  1.2  :  i  in  an  interval  of  10°  C. 

1  Tammann,  Zeitschr.  f.  ph..  Ch.  18.  436  (1895),  gives  /*  =  2  ^  =  5870, 
which  is  evidently  due  to  some  misprint  or  other  error. 


VELOCITY  OF  REACTION.     HOMOGENEOUS  SYSTEMS       49 

Tammann  investigated  also  the  slow  destruction  of  emul- 
sin  in  0.5  per  cent  solution  and  in  the  form  of  dry  powder. 
Even  in  this  case  the  reaction  was  monomolecular.  The 
content  of  emulsin  in  the  solution  or  in  the  powder  at 
different  times  was  determined  by  estimating  its  decom- 
posing influence  on  salicin.  He  found  for  the  solution 
(between  60°  and  75°)  /*  =  45,000,  corresponding  to  an  in- 


DESTRUCTION  OF  A  0.5  PER  CENT  EMULSIN 


TEMP. 

^oba. 

•K"calc. 

40 

0.04 

O.OII 

50 

0.18 

0.099 

60 

0.80 

0.800 

65 

2.86 

2.180 

70 

5-90 

5.740 

75 

14.70 

14.700 

/x  =  45,000 

crease  in  the  proportion  7:1  in  an  interval  of  10  degrees. 
For  the  solid  powder  /x  was  only  26,300;  that  is,  60  per 
cent  of  that  for  the  solution  (the  determination  is  rather 
uncertain).  Furthermore,  the  decomposition  of  the  powder 
at  80.5°  C.  proceeds  about  500  times  more  slowly  than 
that  of  the  0.5  per  cent  solution.  As  will  be  seen  in  the 
following,  rennet  behaves  in  a  similar  manner,  and  it 
seems  to  be  a  very  common  observation  that  the  sub- 
stances with  which  we  are  dealing  are  much  more  resist- 
ing to  heat  in  dried  form  than  in  solution.  This  reminds 


LECTURES  ON  IMMUNITY 


us  in  a  certain  sense  of  the  great  resistance  of  dried 
spores  to  high  temperatures  as  compared  with  the  pro- 
nounced destructive  influence  of  higher  temperatures  on 
developed  bacilli  in  fluid  media. 

Dr.  Euler  has  collected  the  experimental  data l  bearing 
upon  the  catalytic  action  of  ferments.  In  most  cases  we 
find  that  the  influence  of  the  time  of  reaction  may  be 
represented  as  a  monomolecular  process.  Thus,  for 
instance,  he  finds  for  the  decomposition  of  hydrogen 
peroxide  (H2O2)  by  solutions  containing  3.4  or  5  c.c.  of 
the  juice  of  the  Boletus  s caber  to  the  200  c.c.  the  following 
values  at  15°  C.2  q  is  the  quantity  of  H2O2,  determined 
by  titration  with  o.oi  n.  KMn  O4 ;  n  is  the  concentration  of 
the  "  catalase,"  /  time  in  minutes. 


*=3 

«=4 

n=s 

t 

q 

K 

/ 

q 

K 

t 

q 

K 

o 

8.0 



o 

8.0 

__ 

O 

8.2 

. 

6 

6.9 

0.0107 

8 

6.2 

0.0138 

2 

7-5 

0.0193 

12 

5.8 

o.oi  1  6 

10 

5.6 

0.0154 

7 

6.0 

0.0193 

19 

5-0 

0.0107 

13 

5-i 

0.0150 

16 

4.0 

0.0195 

55 

2-5 

O.OIOO 

19 

4.2 

0.0147 

22 

3.15 

0.0190 

0.0107 

0.0147 

0.0193 

The  constant  of  reaction  K,  calculated  for  a  monomo- 
lecular reaction,  increases  with  the  concentration  slightly 
more  than  proportionally.  In  the  same  manner,  accord- 
ing to  the  investigations  of  Bredig  and  M tiller  von  Berneck, 

1  Euler:  "Katalyse  durch  Fermente,"  Zeitschr.  f. ph.  Ch.  45.  420  (1905). 

2  Euler :  "  Zur  Kenntnis  der  Katalasen,"  Beitrage  zur  chemischen  Physi- 
ologie,  7.  h.  1-3  (1905). 


VELOCITY  OF   REACTION.     HOMOGENEOUS  SYSTEMS        51 


behaves  the  catalytic  action  of  a  colloidal  solution  of  plati- 
num on  hydrogen  peroxide. 

In  an  analogous  manner,  according  to  Euler's  measure- 
ments, the  catalase  extracted  from  lard  saponifies  a  con- 
centrated solution  of  ethyl-butyrate  (at  35°C).  q  is  the 
quantity  of  butyric  acid  set  free  after  t  minutes,  as  deter- 
mined by  titration  with  barium  hydrate. 


t 

q 

?«  -q 

K 

0 

0.0 

2.70 



2 

0.30 

2.40 

0.0256 

6 

0-75 

'•95 

0.0235 

9 

1.05 

1.65 

0.0237 

16 

1.65 

1.05 

0.0250 

00 

2.70 

—~ 

-~ 

The  reaction  is  clearly  monomolecular,  as  is  indicated 
by  the  constancy  of  K.  A  more  complicated  formula  was 
found  empirically  by  Henri  1  to  be  valid  for  the  inversion 
of  cane  sugar  by  means  of  invertin  extracted  from  yeast 
cells. 

Henri's  formula  is  the  following  :  — 


a  —  x 


It  differs  from  the  formula  for  monomolecular  reactions 
by  the  expression  (a  -f-  x}  instead  of  simply  a  in  the  nom- 
inator after  log.  As  example  I  quote  the  reaction  of  4c.c. 

solution  of  diastase  with  0.5  n.  sugar  at  25°  C.    '-  is  the 

inverted  sugar  proportional  to  the  initial  quantity  of  cane 
sugar. 

1  V.  Henri:  Zeitschr.  f.  ph.  Ch.  39.  194  (1901). 


LECTURES  ON  IMMUNITY 


t  (rain.) 

X 

a 

i     a 

i   a  +  x 

/'"6  a-  x 

t  *  &rt  —  X 

75 

0.037 

0.000218 

0.00022 

186 

0.103 

254 

24 

499 

0.228 

28l 

25 

505 

0.292 

297 

26 

557 

0.322 

303 

26 

II2O 

0.589 

345 

26 

1172 

0.6  1  1 

350 

26 

Whereas  K  increases  regularly  with  time  in  the  propor- 
tion I  :  1.6,  KI  is  nearly  constant.  The  quantity  trans- 
formed in  a  certain  time  is  proportional  to  the  quantity  of 
diastase  present,  but  no.t  to  the  concentration  of  the 
cane  sugar  in  the  solution.  In  a  rather  large  interval 
(o.  1 5-0.6  n.),  the  transformed  quantity  is  independent  of 
the  concentration  of  cane  sugar,  as  Duclaux  maintained, 
but  at  low  and  high  concentrations  we  get  lower  values 
than  at  mean  concentrations.  At  very  low  concentra- 
tions the  transformed  quantity  is  proportional  to  the 
concentration  of  cane  sugar.1 

In  some  other  cases  also  the  formula  of  Henri  has  been 
verified.  Still  it  seems  probable  that  in  dilute  solutions  of 
sugar  the  reaction  is  of  the  pure  monomolecular  type. 
Only  at  higher  concentrations  do  deviations  occur.  Bar- 
endrecht2  has  suggested  a  very  singular  theory,  according 
to  which  the  deviations  might  be  due  to  an  absorption  by 
the  molecules  of  the  sugar  of  a  kind  of  radiation  emanat- 
ing from  the  enzyme,  which  emanation  is  said  to  produce 


1  Adrian  Brown :  "  Enzyme  Action,"  Journ.  Chem.  Soc.  81.  387  (1902). 

2  Barendrecht :  Zeitscr.  /.  ph.  Ch.  49.  456  (1904). 


VELOCITY  OF   REACTION.     HOMOGENEOUS   SYSTEMS        53 

the  inversion.  This  is  not  the  place  to  enter  upon  a  discus- 
sion of  this  peculiar  view. 

Regarding  the  influence  of  temperature  on  the  action  of 
invertase  on  cane  sugar  we  possess  some  old  observations 
of  Kjeldahl.1  They  give  an  optimum  at  about  52.5°  and 
fji=  9080.  They  are  reproduced  in  the  table: — 

Temp.    o  18   30   40   45   48   50   52.5  55   60   65  70°  C. 
Vel.  obs.  17  60  113  179  228  250  260  267  260  179   21   o 
Vel.  calc.  21  (60)  112  181  (228)  261  285  318  353  436  534  651 

In  a  recent  memoir2  Henri  analyses  the  hydrolysis  of 
maltose  by  means  of  maltase.  In  this  case  the  reaction- 
product  is  glucose,  and  the  constant  of  reaction  increases 
with  the  progress  of  the  reaction.  Henri's  formula 

1C  = -log—     -  gives  a  very  nearly  constant  value  for  K. 

t  d   X 

This  constant  decreases  as  the  quantity  of  maltose  in- 
creases. For  the  first  three  hours  it  is,  for  instance,  for 
solutions  of  the  following  concentration,  2  per  cent  sol. 
K=  368  •  icr5,  4  per  cent  sol.  K—  164  •  io~5,  6  per  cent  sol. 
K=  1 06  •  icr5.  It  is  nearly  inversely  proportional  to  the 
quantity  of  maltose  present.  It  would  therefore  be  reason- 
able to  put — 


where  K^  is  a  new  constant,  and  (a  —  x)  the  concentration 
of  the  maltose.  But  as  the  maltose  as  well  as  the  glucose 
has  a  retarding  influence  on  the  process,  it  would  be  more 
rational  to  put — 

1  Kjeldahl:  cited  from  Duclaux,  Traite  de  microbiologie,  2.    177  (1899). 

2  Victor    Henri:    "  Recherches    physico-chimiques    sur    les    diastases," 
Archive  di  Fisiologia,  2.  i   (Nov.  1904). 


54 


LECTURES   ON  IMMUNITY 


(a— x)  +  nx  dt      (a—x)+nx' 

which,  integrated,  gives  the  formula  of  Bodenstein ; 


In  this  case  we  find  a  sufficient  agreement  with  the  experi- 
mental results,  if  we  suppose  n  —  ^,  as  Henri  has  shown. 
For  invertase  acting  on  saccharose  n  —  0.5,  and  for  emulsin 
acting  on  salicin  n  —  2.  Of  course  the  introduction  of  a 
new  constant  n  is  favourable  to  the  agreement  between  the 
calculation  and  the  observation.  Still  Henri  finds  that  the 
agreement  for  the  maltose  is  not  very  satisfying  (K^  varies 
between  0.028  and  0.046).  - 

Henri  therefore  proposes  to  introduce  still  a  new  em- 
pirical constant  in  the  equation  for  K^.  But  it  is  to  be 
feared  that  the  calculation  will  not  repay  the  work  laid 
out  upon  it  as  long  as  the  experiments  are  so  contradic- 
tory as  now.  For  instance,  I  have  calculated  some  obser- 
vations of  Mr.  Terroine  cited  by  Henri  (I.e.  p.  6)  according 
to  his  formula  and  found  K  very  nearly  constant  =  564-  io~5, 
as  will  be  seen  from  the  following  figures  for  a  2  per  cent 
solution  of  maltose: — 


t  (min.  ) 

*% 

v-  i  ,ioo-fjr 
A  =  -  /  — 

t   100—  X 

V   J  »   I0° 

/  IOO—  X 

62 

0-373 

549.  io-6 

327.IO-6 

90 

0-5I5 

550 

349 

120 

0.656 

569 

389 

150 

0.772 

593 

428 

I76 

0.832 

589 

440 

210 

0.860 

535 

407 

240 

0.914 

561 

444 

362 

0.965 

(483) 

402 

VELOCITY  OF  REACTION.     HOMOGENEOUS  SYSTEMS       55 


According  to  the  figures  of  Terroine  K  does  not  change 
more  than  10  per  cent  (the  last  value,  as  there  are  only  3.5 
per  cent  of  the  matose  left,  is  too  unreliable  to  be  used  for 
the  calculation).  But  in  the  same  memoir,  on  p.  4,  Henri 
gives  values  for  a  2  per  cent  solution  of  maltose  for 
which  the  values  of  K  change  between  3i9-io~5  and 
489  •  io~5  i.e.  53  per  cent.  The  errors  of  observation  must 
therefore  be  very  great,  and  the  figures  should  not  be  ap- 
plied to  delicate  calculations.  Still  greater  is  the  disagree- 
ment in  the  figures  of  Armstrong,1  who  finds  that  the  con- 

MALTOSE  5  %  AT  30°  (E.  F.  ARMSTRONG) 


t  (hours) 

*% 

V        I  ,       100 

Al—  .* 
/   100  —  x 

I 

7-3 

0.0329 

2 

13-9 

0.0325 

4 

24.4 

0.0304 

7.25 

3i-7 

0.0229 

23 

35-2 

0.0082 

stant  Kly  calculated  from  the  formula  for  monomolecular 
reactions,  sinks  with  the  progress  of  the  reaction;  whereas 
Henri  finds  that  K,  calculated  from  his  formula,  is  nearly 
constant;  i.e.  that  K±  as  is  seen  in  the  figures  given  above, 
increases  very  rapidly  with  the  progress  of  the  reaction,  and 
this  is  valid  not  only  for  2  per  cent,  but  in  a  still  higher  de- 
gree for  4  per  cent  and  6  per  cent  solutions.2 

Armstrong  has  communicated  additional  measurements 

1  E.  F.  Armstrong:  Proc.  Roy.  Soc.  73.   508  (1904). 

2  Brown  and  Glendinning  (Journ.  Chem.  Soc.  81.  388,  1902)  find  that  the 
formula  of  Henri's  is  valid  even  for  the  hydrolysis  of  soluble  starch  by  means 
of  diastase. 


LECTURES  ON  IMMUNITY 


on  the  inversion  of  milk  sugar  by  means  of  lactase  or 
emulsin,  which  follow  a  wholly  different  law  from  that  used 
in  Henri 's  formula.  The  regularity  is  evident  only  if  the 
enzyme  is  present  in  great  quantity.  We  reproduce  only 
the  first  two  tables  (I  and  VII)  illustrating  the  hydrolytic 
action  of  100  c.c.  of  lactase-extract  or  0.2  g.  of  emulsin  on 
2  g.  of  milk  sugar  at  36°  C. 


ACTION  OF  LACTASE  ON  M:LK  SUGAR 

ACTION  OF  EMULSIN  ON  MILK  SUGAR 

/  (hours) 

*% 

X 

^7 

t  (hours) 

*% 

X 

^7 

I 

22.1 

22.1 

°-5 

3-2 

4-5 

2 

31.2 

22.O 

I 

4-8 

4-8 

3 

38.9 

22.5 

2 

6.4 

4-5 

4 

45-8 

22.9 

3 

7.6 

4-4 

5 

Sl-5 

23.0 

4-5 

9.0 

4.2 

6 

56.6 

23.1 

6 

1  0.0 

4.1 

10 

69.0 

21.8 

23 

19.7 

4.1 

17 

84.2 

20.4 

29 

22.O 

4.1 

23 

92.4 

19.3 

48 

29.0 

4-2 

29 

95-3 

17.7 

53 

30-7 

4.2 

38 

98.0 

15-9 

144 

62.2 

5-2 

264 

77-5 

2.9 

Here  the  quantity  transformed  is  very  nearly  propor- 
tional to  the  square  root  of  the  time  of  action.  This  cor- 
responds to  the  differential  equation 


d*  ' 

dt 


x      x  (a—x) 


or,  in  other  words,  the  reaction-constant  calculated  with  the 
common  formula  for  a  monomolecular  reaction  should  be 
inversely  proportional  to  the  product  of  the  rest  of  the 
milk  sugar  and  of  the  reaction-products.  This  will  happen, 


VELOCITY   OF   REACTION.     HOMOGENEOUS  SYSTEMS        57 


provided  that  the  reaction-products  are  present  in  sufficient 
quantity,  and  that  one  molecule  of  the  milk  sugar  and  one 
molecule  of  the  reaction-products  unite  with  one  molecule 
of  the  enzyme  to  form  a  partially  dissociable  compound. 

It  has  been  long  known  that  the  enzymes  differ  from 
chemical  catalysors  in  one  very  important  point.  This 
experiment  was  done  in  1883  by  Duclaux,1  with  solutions 
containing  10,  20,  and  40  resp.  g.  of  sugar.  In  100  c.c. 
dissolve  20  mg.  of  invertase  and  elevate  the  temperature 
to  37°  C. ;  then  after  four  hours  we  shall  find  that  nearly 
the  same  quantity  of  sugar  (about  5  g.)  will  be  hydrolysed 
in  the  three  cases ;  whereas  if  we  had  added  20  mg.  of  an 
acid,  the  inverted  quantity  would  have  been  2.5  and  5  g. 
in  the  two  first  cases,  if  it  was  10  g.  in  the  last.  Arm- 
strong2 gives  some  good  instances  of  this  regularity, 
which  holds  only  if  the  quantity  of  enzyme  is  small.  The 
tabulated  quantity  is  the  number  of  grammes  of  hydrolysed 
milk  sugar  in  100  c.c. 


SOLUTION  CONTAINING 
%  MILK  SUGAR 

GRAMMES  MILK  SUGAR,  HYDROLYSED 
BY  A  SMALL  QUANTITY  OF  LACTASE  IN 

GRAMMES    MILK   SUGAR, 
HYDROLYSED  BY  A  SMALL 
QUANTITY  OF  EMULSIN  IN 

24  h. 

46  h. 

144  h. 

23  h. 

48  h. 

10 

1.42 

2.22 

3.34 

1.97 

2.98 

20 

I.4I 

2.18 

3.38 

2.12 

3-06 

40 

1.44 

2.21 

3-30 

2.10 

3.06 

On  the  other  hand,  if  there  is  present  a  great  quantity  of 
enzyme  and  a  relatively  small  quantity  of  sugar,  the  action 
is  proportional  to  this  latter  quantity,  just  as  if  an  acid 
acted. 

1  Duclaux:    Traite  de  microbiologie,  2.  136  (1899). 

2  Armstrong:  /.  c.t  pp.  508-510. 


58  LECTURES  ON  IMMUNITY 

ACTION  OF  INVERTASE  ON  100  c.c.  OF  SUGAR  SOLUTION  (BROWN) l 


PER  CENT  SACCHAROSE 


GRAMMES  INVERTED  IN  i  H. 


0.25 

°-5 
i.o 


0.060 
0.129 
0.249 


ACTION  OF  LACTASE  ON  100  c.c.  OF  MILK  SUGAR  SOLUTION  (ARMSTRONG) 


PER  CENT  MILK  SUGAR 


AMOUNT  CHANGED  IN  3  H. 


0.2 


I.O 


0.042 
0.098 
0.185 


If  the  enzyme  is  present  in  small  proportion,  the  trans- 
formed quantity  is  proportional  to  its  quantity,  as  is  seen 
from  the  following  experiments  of  O'Sullivan  and  Tomp- 
son2  and  Armstrong. 

HYDROLYSIS  OF  CANE  SUGAR  TO  78  PER  CENT  BY  MEANS  OF 

INVERTASE  AT  15.5°  (O'SULLIVAN  AND  TOMPSON) 

0.15  g.  inv.  time  283   min.  (calc.  307  ) 

0.45  g.  inv.  time  94.8  min.  (calc.  92.1) 

1.5     g.  inv.  time  30.7  min.  (calc.  30.7) 

HYDROLYSIS  OF  A  5  PER  CENT  SOLUTION  OF  MILK  SUGAR  (looc.c.) 


SOLUTION  CONTAINING 


AFTER  24  HOURS 


0.66  c.c.  of  lactase 

1  c.c.  of  lactase 

2  c.c.  of  lactase 
5        c.c.  of  lactase 


OBS.  CALC. 

2.3  p.  C.  2.1 

3.2  p.  c.  3.1 

6.3  p.  c.  6.2 
15.4  p.  c.  15.5 


1  Brown:  Journ.  Chent.  Soc.  81.  387  (1902). 

2  O'Sullivan  and  Tompson :  Journ.  Chem.  Soc.  57.  865  (1890). 


VELOCITY  OF   REACTION.     HOMOGENEOUS   SYSTEMS        59 

A  very  good  instance  is  given  by  Henri  l  of  the  in- 
version of  cane  sugar  by  means  of  invertase  at  constant 
concentration.  The  following  table  gives  the  number  (n) 
of  milligrammes  inverted  during  the  first  minute  of  solu- 
tions of  cane  sugar  of  the  concentration,  c.  normal  ( i  normal 
=  342  g.  per  liter). 

c  =  o.oi      0.025      o<°5        Otl      °-25       °-5         l     l*S          2 
n  =  0.58      1.41        2.40      2.96      4.65      5.04    4.45     2.82     1.15 

As  will  be  seen  from  these  figures  n  is  at  first  nearly 
proportional  to  c,  then  it  reaches  a  maximum  at  c  =  o.5,  only 
later  on  to  sink  again  at  very  high  concentrations,  at 
which  the  solvent  may  be  regarded  as  changed. 

In  good  agreement  with  this  experience  Terroine  found 
that  the  quantity  of  maltose  transformed  by  means  of  a 
given  quantity  of  maltase  in  a  100  c.c.  of  solution  is  nearly 
proportional  to  the  concentration  of  the  maltose  until  it 
reaches  about  2  per  cent  and  is  thereafter  independent  of  the 
concentration.  This  regularity  may  be  detected  in  some 
experiments  executed  by  Tammann  as  early  as  in  1889,  on 
the  decomposition  of  different  quantities  of  amygdalin 
by  means  of  a  constant  quantity  of  emulsin.2  All  these 

DECOMPOSITION  OF  AMYGDALIN  (IN  GRAMMES)  BY  MEANS  OF  EMULSIN 

Quantity  of  amygdalin  2-555  5-11  10.229 

Time  (min.)  =  14  0.61  0.61  0.50 

19  0.77  0.85  0.73 

23  0.79  0.98  0.86 

experiments  lead  us  to  the  assumption  that  the  substance 
which  really  is  decomposed  into  the  reaction-products  is  in 

1  Henri:  "Lois  generals  de  1'action  les  disastases:  These,"  Paris  (1899). 

2  Tammann :   Zeitschr.  f.  ph.  Ch.  3.  33  (1889) ;  Hoppe  Seylers  Ztitschr.  16. 
315  (1892). 


60  LECTURES  ON  IMMUNITY 

these  cases  a  compound  of  the  enzyme  and  the  substrate 
upon  which  it  acts.  If  the  enzyme  is  in  excess  (in  the 
said  cases),  nearly  the  whole  quantity  of  the  substrate 
acted  upon  enters  into  the  compound,  the  quantity  of  which 
is  therefore  proportional  to  the  quantity  of  this  substrate. 
If,  on  the  other  hand,  the  substrate  is  in  excess,  the  quan- 
tity of  compound  is  nearly  proportional  to  the  quantity  of 
enzyme.  We  may  therefore  from  these  experiments  draw 
conclusions  as  to  the  quantities  of  enzyme  that  are  equiva- 
lent to  a  certain  quantity  of,  e.g.,  sugar  or  milk  sugar. 
These  conclusions  indicate  that  the  equivalent  weights  of 
the  enzymes  are  not  so  high  as  is  often  assumed.  The 
circumstance  that  enzymes  are  not  in  general  pure  sub- 
stances hinders  the  estimation  of  their  true  equivalent 
weights. 

The  formula  of  Bodenstein  and  Henri  may  be  deduced 
in  the  following  manner.  The  quantity1  of  ferment  from 
the  beginning  may  be  called  F,  that  of  the  decomposing 
substance  A.  Of  this  a  part,  x,  may  be  decomposed  so 
that  only  A  —  x  remains.  The  ferment,  substance  A,  and 
reaction-products  may  enter  into  compounds  consisting  of 
i  molecule  of  ferment  with/*  molecules  of  A  and  q  mole- 
cules of  different  reaction-products.  Of  these  compounds 
z,  zlt  etc.,  molecules  may  be  present.  Then  for  every  one 
of  these  kinds  of  molecules  a  formula  of  the  following 
form  is  valid  :  — 
2  =  klFl(A-x-  2/*)»  (x  -  2?*)«  where  F=  F1  +  2*. 

If  we  suppose  ^.z  to  be  small  as  compared  with  A  and 
x,  we  get  —  z  =  kFl  (A  - 


1  Cf.  Henri  :  Compt,  rwd<  135.  916. 


VELOCITY  OF   REACTION.     HOMOGENEOUS   SYSTEMS       6  1 

Further  we  have  :  — 


In  many  cases  the  first  term,  i,  in  the  denominator  is 
little  as  compared  with  the  terms  under  the  sign  of  sum- 
mation and  may  therefore  be  neglected.  In  this  case  we 
get  the  formula  of  Bodenstein  if  we  put  n  —  i,  and  suppose 
the  terms  under  2  to  be  two,  one  in  which  /=  i  and  g  =  o, 
another  in  which  /  =  o  and  q—\.  In  nearly  all  cases 
hitherto  investigated  the  velocity  of  reaction  is  nearly  pro- 
portional to  the  first  power  of  the  concentration  of  enzyme 
present;  therefore  the  deduction  is  given  only  for  this 
case.  The  more  general  formula,  in  which  this  concentra- 
tion enters  to  another  power  than  I,  is  very  complicated. 
A  very  common  case  is  that  in  which  only  one  term  with 
/=o  and  q=  i  enters  under  the  sign  2  ;  this  is  the  case 
in  the  digestion  of  egg-white  by  pepsin  and  trypsin  and 
for  the  hydrolysis  of  fat  by  means  of  lipases.  Here  also 
the  term  i  may  be  dismissed.  This  holds  good  even  for 
the  experiments  of  Armstrong,  in  which  the  product  of 
reaction  is  proportional  to  the  square  root  of  the  time  of 
reaction.  Here/  =  i  and  4=1,  i.e.  the  chief  influence  is 
due  to  the  formation  of  a  compound  between  the  enzyme, 
the  reaction-product,  and  the  original  substance.  The  for- 
mula is  evidently  not  valid,  if  the  quantity  of  substance 
acted  upon  by  the  enzyme  or  the  reaction-product  is  to  a 
great  part  bound  by  the  enzyme.  Therefore  the  formula 
gives  no  good  values  for  the  experiments  of  Terroine  with 
small  quantities  of  maltose.  It  will  be  necessary  to  carry 
out  a  large  number  of  experiments  in  order  to  verify  this 


62  LECTURES  ON   IMMUNITY 

view,  which  seems  to  be  the  best  expression  of  our  pres- 
ent knowledge. 

A  very  prominent  place  in  this  connection  is  held  by 
the  rule  of  Schiitz,  according  to  which  some  processes, 
especially  the  peptic  digestion,  proceeds  through  a  certain 
time  nearly  proportionally  to  the  square  root  of  the  time 
and  thereafter  more  slowly. 

To  understand  the  meaning  of  this  rule,  we  at  first 
examine  a  very  well-known  process,  the  saponification  of 
ethyl-acetate  by  means  of  ammonia,  on  which  I  have 
carried  out  some  experiments.  A  mixture  was  made  of 
1 8  c.c.  distilled  water  and  I  c.c.  (  =  0.91  grammes)  of 
ethyl-acetate,  in  a  vessel  used  for  determining  conductivi- 
ties, held  at  a  constant  temperature  (16°  C.).  At  a  certain 
moment  I  c.c.  of  a  0.02  normal  solution  of  ammonia  was 
added  and  the  vessel  shaken.  Afterwards  the  resistance 
was  determined.  It  decreased  at  first  rapidly,  then  slowly, 
indicating  that  the  well-conducting  acetate  of  ammonia 
was  formed  from  the  less-conducting  ammonia,  according 
to  the  equation  :  — 

NH3  +  CH3COO  C2H5  +  H2O  =  NH4CH3COO  +  C2H5OH. 

By  means  of  the  conductivity  the  progress  of  the  chem- 
ical process  was  determined.  If  we  take  the  quantity  of 
ammonia  at  the  beginning,  like  1000,  then  the  following 
quantities  of  ammonium-acetate,  ;roba.,  were  observed  at  the 
given  times  (t  in  minutes). 

The  table  contains  two  calculated  values  of  x,  viz.  ^calc<  , 
found  by  means  of  a  formula  given  below,  and  ;rcalc<  2, 
deduced  by  means  of  Schiitz's  rule.  At  ^=14  the  latter 
quantity  exceeds  1000,  which  is  evidently  impossible. 


VELOCITY  OF   REACTION.     HOMOGENEOUS  SYSTEMS        63 


PROGRESS  OF  SAPONIFICATION  OF  ETHYLACETATE  BY  MEANS  OF  AMMONIA 

AT  1 6°  C. 


t 

Xobt. 

.Tcalc.l 

•Zoslc.2 

I 

320 

352 

303 

i-5 

394 

4I2 

371 

2 

453 

469 

428 

3 

539 

548 

525 

4 

607 

608 

606 

5 

657 

656 

677 

6 

701 

685 

742 

7 

733 

728 

801 

8 

764 

757 

856 

10 

810 

803 

958 

H 

878 

864 



20 

936 

923 



32    - 

980 

973 



The  agreement  with  Schiitz's  rule  is  rather  imperfect, 
especially  for  high  values  of  x.  This  is  a  general  feature 
of  the  said  rule,  and  it  is  quite  clear  that  the  rule  would 
give  values  of  x  exceeding  1000  for  high  values  of  /,  which 
is  evidently  impossible. 

In  order  to  deduce  a  rational  formula  for  this  process, 
we  must  remember  that  the  saponification  is  a  catalytic 
process,  with  a  specific  velocity  of  reaction  proportional  to 
the  concentration  of  the  hydroxyl-ions  and  of  the  ethyl- 
acetate.  This  latter  is  here  present  in  such  an  excess, 
that  only  about  0.2  per  cent  of  it  is  transformed  during 
the  process,  consequently  its  concentration  may  be  taken 
as  a  constant  (P).  The  concentration  y  of  the  hydroxyl- 
ions  is  subject  to  the  following  formula:  — 

K(A~x\ 

"'~~ — - — i — '' 
ky 


64  LECTURES  ON  IMMUNITY 

where  A  is  the  quantity  of  ammonia  present  at  the 
time  /  =  o,  x  the  quantity  of  ammonium-acetate  formed, 
and  consequently  A—x  the  quantity  of  ammonia  at  a 

given  time,  t.  The  velocity  of  reaction  —  is  propor- 
tional to  y  and  to  the  quantity  P  of  ethyl-acetate,  so  that 

the  equation 

dx  =  K(A-x) 

dt        x  +  ky 

is  also  valid.  If  x  is  not  too  small,  ky  may  be  neglected, 
and  we  find  the  integral :  — 


From  this  formula  the  values  ;rcalc-1  are  calculated.  A 
is  set  as  1000.  Here  KP  is  82.  The  agreement  may  be 
regarded  as  very  satisfying.  At  low  values  of  t  the 
observed  value  x  is  less  than  the  calculated  one,  due  to  the 
neglection  of  ky,  as  compared  with  x,  which  is  not  allowed 
if  x  is  small. 

If  x  is  very  small  compared  with  A,  i.e.  in  the  beginning 
of  the  experiment,  we  may  as  a  first  approximation  put 

A  —  x  =  A  and 

dsc=KAP 

dt          x 
which  gives  —  x*  =  KAP, 

x  is  proportional  to  the  square  root  of  the  time  and  also 
to  the  square  root  of  the  concentration  of  the  ammonia  at 
the  beginning  of  the  experiment,  and  to  the  square  root 
of  the  concentration  of  the  ethyl-acetate.  This  is  the  rule 
of  Schiitz. 

As  is  seen  from  these  equations,  x  is  only  a  function  of 


VELOCITY  OF   REACTION.     HOMOGENEOUS   SYSTEMS       65 

APt,  i.e.  of  the  product  of  the  initial  concentration  of  the 
catalytic  agent  —  here  ammonia  —  of  the  substrate  —  here 
ethyl-acetate  —  and  of  time.  Evidently  here  the  product 
KP  may  be  regarded  as  the  constant  of  the  reaction. 

From  the  analysis  given  above  we  find  that  the  validity 
of  the  rule  of  Schiitz  indicates  that  the  active  part  of  the 
catalysor,  ammonia  or  pepsin,  etc.,  is  inversely  propor- 
tional to  the  products  formed.  This  occurs  in  the  case  of 
ammonia  because  the  product,  NH4-ions,  gives  a  com- 
pound with  the  active  part,  the  hydroxyl-ions,  which  is  dis- 
sociated to  a  very  low  degree.  Probably  the  case  is  similar 
in  all  the  processes  in  homogeneous  media  studied  below 
and  belonging  to  this  group  (peptic  or  tryptic  digestion). 
In  heterogeneous  media  other  circumstances,  such  as 
change  of  solubility,  may  play  a  role ;  perhaps  this  occurs 
in  the  saponification  by  means  of  lipases. 

One  of  the  most  interesting  investigations  in  this  line  was 
done  as  early  as  1895  by  Sjoqvist.1  He  dissolved  2.23  g. 
of  egg-albumen,  which  by  dialysis  had  been  nearly  puri- 
fied from  salts,  in  100  c.c.  of  four  solutions,  which  further- 
more contained  0.005  gramme-molecules  (=0.1875  g.) 
HC1  and  2.5,  5,  10,  or  20  c.c.  of  pepsin.  In  this  homo- 
geneous system  the  albumen  slowly  digested  at  37°  C.  At 
the  same  time  the  conductivity  gradually  diminished,  and 
this  diminution  was  regarded  as  a  measure  of  the  velocity 
of  digestion.  At  given  intervals  samples  were  taken  from 
the  solution  and  rapidily  cooled  to  1 8°  C.,  at  which  tem- 
perature the  velocity  of  digestion  might  be  practically 
neglected.  The  determination  of  the  conductivity  was 
made  at  this  temperature  in  the  ordinary  manner. 

1  Sjoqvist  :  Skandinav.  Archivf.  Physiologie,  5  (1895). 
F 


66 


LECTURES  ON  IMMUNITY 


He  found  the  following  figures  :  p  is  the  conductivity, 
A  its  decrease,  Acalc.  the  corresponding  calculated  quantity, 

*J   *}  ^  fi\  A. 

and /  =  -~* ,  where  P  is  the  concentration  of  pepsin. 

VP 

DIGESTION  OF  EGG-ALBUMEN  AT  37°  C.  BY  MEANS  OF  HCL  AND  PEPSIN 


/>=0.025  % 

/>=o.os  % 

TIME 
(hours) 

A* 

A 

*cal. 

/ 

* 

A 

Acal, 

/ 

0 

188.4 

— 

— 

— 

188.4 

— 



— 

0.5 

— 

— 

5-3 

— 

— 

— 

7.8 

— 

I 

— 

— 

7-8 

— 

178.2 

10.2 

10.5 

120 

2 

177-3 

II.  I 

10.5 

157 

172.8 

I5.6 

I5.6 

I56 

4 

171.1 

17-3 

15.6 

245 

164.7 

23.7 

21.6 

237 

6 

167.4 

21.  0 

(19.6) 

297 

159-5 

28.9 

(26.9) 

289 

8 

164.5 

(23.9) 

21.6 

338 

155-5 

(32.9) 

29.7 

329 

9 

163.1 

25-3 

(23-0) 

358 

153-5 

34-9 

(33-7) 

349 

12 

159-9 

28.5 

(26.9) 

403 

149.4 

39-o 

(36-6) 

390 

16 

156.4 

(32.0) 

29.7 

452 

145.2 

(43-2) 

41.6 

432 

20 

152.9 

35.5 

(34-7) 

502 

I4I.O 

47-4 

(46.8) 

474 

32 

146.2 

42.2 

(41-6) 

597 

I33-I 

55-3 

(53-0 

553 

48 

139.8 

(48.6) 

(48.8) 

673 

126.2 

(62.2) 

(61.2) 

622 

64 

135-0 

(53-4) 

53.1 

755 

I2I.4 

(67.0) 

68.2 

670 

96 

127.9 

60.5 

(61.2) 

856 

114.4 

74-o 

(77-o) 

740 

/>=O.I% 

P=0.2% 

TIME 

A 

. 

*' 

A 

- 

(hours) 

** 

Acalc. 

/* 

calc. 

•'" 

0 

188.4 

— 

— 

— 

188.4 

— 

— 

— 

°-5 

179.2 

9.2 

10.5 

65 

176.0 

12.4 

I5.6 

62 

i 

174.2 

14.2 

I5.6 

100 

167.8 

20.6 

21.6 

103 

2 

165.9 

22.5 

21.6 

1  60 

157.9 

30.3 

29.7 

'53 

4 

154.8 

33-6 

29.7 

237 

144-5 

43.9 

41.6 

220 

6 

148.0 

40.4 

(36.6) 

286 

137-2 

51.2 

49-2 

256 

8 

143.2 

(45-2) 

41-6 

320 

133-0 

(55-4) 

53.1 

277 

9 

140.8 

47-6 

(44-5) 

337 

I30.I 

58.3 

55-7 

292 

12 

136.1 

52.3 

49.2 

370 

125.8 

62.6 

61.1 

313 

16 

130.9 

(57-5) 

53-1 

407 

121.  6 

(66.8) 

68.2 

334 

20 

125.7 

62.7 

(58.6) 

443 

117-3 

71.1 

73-3 

356 

32 

119.4 

(69.0) 

68.2 

488 

109.8 

78.6 

83-7 

393 

48 

113.1 

75-3 

(77-o) 

533 

102.3 

86.1 

91.8 

43  * 

64 

109.1 

(79-3) 

83-7 

561 

97-4 

(91.0) 

96.5 

455 

96 

101.8 

86.6 

91.8 

612 

91.2 

97.2 

101.4 

486 

VELOCITY  OF  REACTION.   HOMOGENEOUS  SYSTEMS     67 

The  figures  in  brackets  are  interpolated.  KP  —  125,  if 
P  is  expressed  in  per  cent ;  and  A  —  1000. 

Sjoqvist  found  that  f  was  nearly  constant  for  constant 
and  small  values  of  t:  in  other  words,  the  quantity  of 
transformed  egg-albumen  is  proportional  to  the  square 
root  of  the  acting  pepsin.  But  there  is  also  another  rela- 
tion which  holds  good  even  for  long  times  of  reaction : 
the  digested  quantity  of  albumen  is  a  function  of  Pt  only, 
i.e.  the  quantity  n  of  pepsin  digests  the  same  quantity  in 

the  time  -,  as  the  unit  quantity  of  pepsin  in  the  time  t. 
This  is  seen  from  the  following  table  :  — 


/ 

V=o.o5 

O.I 

O.2 

0.4 

0- 

8 

1.6 

3-2 

4.8 

6-4 

9.6 

P=O.O2$ 

n.  i 

17-3 

23-9 

32.0 

42. 

2 

53-4 

— 

— 

— 

— 

0.05 

10.2 

I5.6 

23-7 

32-9 

43- 

2 

55-3 

67.0 

74.0 

— 

— 

O.I 

9.2 

14.2 

22.5 

33-6 

45- 

2 

57-5 

69.0 

75-3 

79-3 

86.6 

0.2 

— 

I2.4 

20.6 

30.3 

43- 

7 

55-4 

66.8 

73-6 

78.6 

86.1 

Mean 

IO.2 

14.9 

22.7 

32.2 

43- 

8 

55-4 

67.6 

74-3 

79.0 

8M 

V 

II 

I5.6 

22 

3I.I 

44 

From  this  it  follows,  as  is  seen  in  the  mean  values,  that 
if  Pt  does  not  exceed  a  certain  value  (i.o)  the  quantity  of 
digested  albumen  is  nearly  proportional  to  the  square  root 
of  Pt,  as  is  also  seen  from  the  calculated  values  (F)  written 
below  the  means. 

This  was  already  observed  by  Emil  Schiitz l  and  has  been 
confirmed  by  Jul.  Schiitz,2  who  dissolved  the  quantity,  /,  of 
pepsin,  10  c.c.  of  egg-albumen  (containing  1-1.2  g.  of  co- 
agulable  substance),  and  29  c.c.  I  per  cent  HC1  in  100  c.c. 
In  a  digestion  of  15  hours  at  38°  he  found  the  following 
digested  quantities,  d,  of  egg-albumen,  i.e.  pepton,  which  is 
not  coagulable :  — 

1  Emil  Schutz:  Zeitschr.f. ph.  Ch.  9.  577  (1885). 

2  Jul.  Schutz:   Zeitschr.f. ph.  Ch.  30.  I  (1900). 


68 


LECTURES   ON   IMMUNITY 


g> 

^•obs. 

*cal. 

I 

0.0212 

0.0213 

4 

O.O47I 

0.0426 

9 

0.0652 

0.0639 

16 

0.0799 

0.0852 

25 

0.0935 

0.1065 

36 

O.IO3I 

0.1278 

Here  we  have  a  very  nice  example  of  a  monomolecular 
reaction,  where  the  rate  of  transformation  is  proportional 
as  well  to  the  quantity  of  pepsin  present  as  to  that  of 
the  albumen  present,  but  where,  because  of  the  perturbing 
influence  of  one  of  the  reaction-products,  the  simple  law 
of  the  monomolecular  processes  is  altered.  It  reminds  one 
in  this  regard  strongly  of  the  monomolecular  process  of 
transformation  of  acetamid  studied  by  Ostwald,1  or  of  the 
bimolecular  process  of  saponification  of  ethyl  acetate  by 
ammonia,  examined  by  myself.2 

In  such  cases  the  experimental  fact  that  x,  the  trans- 
formed quantity,  is  only  a  function  of  qt,  the  product  of 
the  quantity  of  the  reacting  substance  and  the  time,  gives 
an  answer  to  the  question,  whether  the  action  is,  ceteris 
paribus,  proportional  to  the  quantity,  qy  of  the  reacting 
substance.  In  an  analogous  manner  if  x  is  only  dependent 
upon  (ft  or  generally  upon/(^y,  this  circumstance  indicates 
that  the  action  of  the  substance  is  proportional  to  its 
square  or  in  general  q  to  the  function/^). 

By  the  aid  of  the  integral  formula  the  calculated 
values  are  found  which  are  tabulated  above  beside  those 
found  by  Sjoqvist.  The  agreement  is  very  close  and 

1  Ostwald:  Journ.  f.  prakt.  Ck.  27.  I  (1883). 

2  Arrhenius:   Ztitschr.  f.  ph.  Ch.  2.  289  (1888). 


VELOCITY  OF   REACTION.     HOMOGENEOUS  SYSTEMS       69 

indicates  that  the  method  of  Sjoqvist  was  very  useful  and 
even  that  the  theoretical  views  are  rather  concordant 
with  the  facts.  It  would  have  been  desirable  to  have 
varied  the  quantity  of  hydrochloric  acid  in  these  experi- 
ments. Some  experiments  of  Sjoqvist  on  the  digestion 
in  the  presence  of  other  acids  than  HC1,  namely,  sul- 
phuric, nitric,  and  phosphoric  acid,  seem  to  indicate  that 
the  action  of  these  acids  is  (about  16,  24,  and  37  per  cent 
respectively)  less  than  that  of  hydrochloric  acid ;  but  more 
empirical  material  is  desirable  before  definite  conclusions 
may  be  induced. 

E.  Schiitz  and  Huppert l  have  made  a  large  number  of 
measurements  of  the  digestion  of  egg-white  by  means  of 
hydrochloric  acid  and  pepsin.  The  egg-white  was  freed 
of  globulins.  The  influence  of  the  concentration  of  acid 
was  such  that  if  i  g.  of  egg-white  in  100  c.c.  was  digested, 
the  digested  quantity  in  a  given  time  increased  with  the 
quantity  of  acid,  but  more  slowly  than  proportionally  to  this, 
until  its  concentration  was  0.2  percent;  thereafter  it  was 
nearly  constant,  or  in  some  cases,  even  decreased  a  little. 
This  agrees  with  the  opinion  that  the  really  reacting  sub- 
stance is  the  albuminat-ion,  but  further  investigations  are 
necessary  before  this  may  be  stated  with  certainty. 

In  another  series  of  experiments  the  temperature  was 
varied.  The  digested  quantity  of  0.922  g.  egg-white  in 
100  c.c.  of  0.2  per  cent  HC1  was  found  to  be :  — 

At  30°    C.  0.544  g.  =  59.0  per  cent  Calc.  59.0  per  cent 

"  35      "  0.660  "      71.6        "  "  71.4        " 

"  27.5    «  0.713  «      77.3        «  «  77.4        « 

"  40      "  0.775  "      83-°        "  "  83.0 

1  Schutz  and  Huppert :  Pfliiger's  Arcbiv.  80.  470  (1900). 


LECTURES  ON  IMMUNITY 


By  means  of  the  formula  used  for  the  calculation  of 
peptic  digestion  I  have  determined  /&,  which  was  found  to 
be  15,570,  and  from  this  value  I  have  deduced  the  calcu- 
lated values  given  above.  The  agreement  is  very  satisfac- 
tory, but  additional  investigations  will  be  necessary  to  give 
a  definite  value  for  p.  According  to  Schiitz  and  Huppert 
the  process  has  an  optimum  at  about  50°  C. 

On  analogous  topics  many  interesting  experiments  have 
been  carried  out  in  the  Danish  Serum  Institute.  Different 
quantities  (q  c.c.)  of  pepsin  were  added  to  a  solution  of 
2  c.c.  of  7  per  cent  thymolgelatin,  i  c.c.  0.4  per  cent  solu- 
tion of  HC1,  and  i  —  q  c.c.  of  i  per  cent  solution  of  NaCl. 
The  liquid  was  thereafter  well  mixed,  and  the  whole  was 
put  in  a  test-tube  which  was  placed  in  a  thermostat  at 
36.6°  C,  and  held  at  this  temperature  during  a  certain  time, 
/.  Then  the  test-tube  was  placed  on  ice  until  the  next  day. 
In  this  manner  different  test-tubes  with  varying  q  were 
prepared.  The  contents  of  tubes  with  high  q  were  liquefied. 
It  was  noted  which  value  of  q  was  just  high  enough  to 
produce  liquefaction.  In  this  way  the  following  table  was 
found :  — 

DIGESTING  INFLUENCE  OF  PEPSIN  ON  THYMOLGELATIN 


t  (hours) 

9 

q.t 

t  (hours) 

q 

q.t 

i-33 

0.6 

0.8 

8 

0.13 

1.04 

2 

0.47 

0.94 

10 

0.095 

0-95 

3 

0-3 

0.9 

12 

0.08 

0.96 

4 

0.26 

1.04 

14 

0.07 

0.98 

6 

0.18 

1.  08 

20 

0.045 

0.90 

24 

0.038 

0.91 

The  mean  value  is  q  •  t  =  0.96,  and  the  observed  values 


VELOCITY  OF  REACTION.     HOMOGENEOUS   SYSTEMS       71 

do  not  vary  from  it  more  than  may  be  attributed  to  the  ex- 
perimental errors. 

In  quite  the   same  manner  experiments  were  done  at 

different  temperatures,  and  the  observed  values  of  K  =-— 

compared  with  the  values  calculated  from  the  formula  above 
(ji—  10,750).    The  results  are  tabulated  below  :  — 

INFLUENCE  OF  TEMPERATURE  ON  THE  DIGESTION  OF  THYMOLGELATIN 


TEMP. 

^obs. 

•^calc. 

2O 

0.36 

0.36 

25 

0.45 

0.48 

29.8 

0.62 

0.65 

36.8 

I.OO 

0.96 

40.7 

1.  20 

1.  21 

Segelcke  and  Storch *  had  already  stated  that  a  solution 
of  rennet  coagulates  milk  in  times  which  are  inversely 
proportional  to  the  concentration  of  the  solution.  Soxhlet 
confirmed  these  results  by  more  accurate  measurements. 
On  the  basis  of  the  proportionality  of  the  digestion  and  the 
coagulating  power  of  peptic  solutions  of  different  prepara- 
tion Pawlow  concluded  that  rennet  is  probably  identical 
with  pepsin.  Hammarsten  objected  to  Pawlow's  opinion, 
because  the  pepsin  was  said  to  follow  the  rule  of  Schiitz, 
which  was  not  the  case  with  the  rennet,  according  to 
Soxhlet's  experiments.  This  contradiction  is  evidently 
not  proved  and  Saw]  alow  therefore  infers  that  all  experi- 
ments are  in  favour  of  Pawlow's  opinion.  Recent  investi- 
gations of  Bang,  Hemmeter,  and  Schmidt-Nielsen  (cf. 
Chapter  IX)  seem  to  indicate  that  pepsin  in  acid  solution 

1  Segelcke  and  Storch  :    Ugeskrift  for  Landmaend  (1870). 


LECTURES  ON  IMMUNITY 


coagulates  casein,  just  as  rennet  in  neutral,  or  even  in  acid 
solution.  The  two  coagulating  enzymes  are  therefore  not 
identical. 

The  influence  of  rennet  on  the  coagulation  of  milk  has 
been  investigated  in  a  manner  analogous  to  that  used  in 
the  study  of  pepsin.  Thus,  for  instance,  Madsen  adds  dif- 
ferent quantities,  q,  of  rennet  to  a  given  quantity  of  milk. 
Then  he  places  the  mixtures  in  test-tubes  and  places  these 
during  a  time,  /,  in  a  thermostat  at  given  temperature. 
After  this  the  tubes  are  rapidly  cooled,  and  it  is  deter- 
mined which  is  the  least  quantity,  q,  sufficing  for  coagula- 
tion. The  results  are  quite  concordant  with  those  for 
pepsin,  as  indicated  by  the  following  table :  — 

COAGULATING   POWER   OF   DIFFERENT   CONCENTRATIONS   OF   RENNET    IN 
MILK  AT  36.55°  C. 


/  (min.) 

f 

qt 

/ 

9 

qt 

4 

0.08 

0.32 

35 

0.007 

0.25 

6 

0.05 

0.30 

5° 

0.005 

0.25 

9 

0.033 

0.30 

70 

0.004 

0.28 

ii 

0.024 

0.26 

80 

0.0032 

0.26 

12 

0.019 

0.23 

100 

O.OO28 

0.28 

14 

0.0175 

0.25 

120 

O.OO25 

0.30 

20 

O.OI3 

0.26 

1  80 

0.00185 

0-33 

25 

0.01 

0.25 

240 

0.0017 

0.41 

30 

0.007 

0.21 

The  mean  value  of  qt  is  0.28  (or  if  the  two  last  ob- 
servations are  excluded  0.267).  The  last  values  display 
a  notable  increase  of  qt,  that  is,  a  decrease  in  the  velocity 
of  reaction  with  increasing  time.  This  agrees  well  with 
the  other  series  of  observations  from  Copenhagen,  as  well 


VELOCITY  OF  REACTION.     HOMOGENEOUS   SYSTEMS       73 


as  with  those  of   other  observers,  and  may  perhaps  be 
ascribed  to  an  attenuation  of  the  rennet  with  time. 

The  influence  of  temperature  on  the  coagulating  power 
of  rennet  was  investigated  by  Fuld.1  He  found  the  fol- 
lowing values  of  the  time  of  coagulation,  /,  for  the  same 
quantity  of  rennet :  — 


TEMPERATURE 

/  (sec.) 

^obs. 

•K*calc. 

25-05 

54 

•185 

I8S 

30 

32 

312 

327 

35 

17 

588 

574 

140 

10.2 

980 

980 

44 

9 

IIII 

1491 

5° 

14.7 

680 

2742 

fi  =  20,650 

The  values  of  l£oba,  are  10,000  divided  by  t.  They  agree 
quite  well  with  the  calculated  values  up  to  a  temperature 
of  40°  C. ;  above  this  the  agreement  fails.  This  evidently 
depends  on  the  fact  that  above  40°  C.  the  destruction  of 
the  rennet  proceeds  at  such  a  speed  that  the  observations 
are  disturbed  thereby.  This  explains  also  the  occurrence 
of  an  optimum  at  about  44°  C.,  which  optimum  therefore 
must  not  be  regarded  as  real.  The  observed  effect  de- 
pends upon  /z  being  many  times  greater  (in  this  case  4.4 
times)  for  the  spontaneous  destruction  than  for  the  pro- 
cess of  fermentation.  The  same  observation  may  be 
applied  to  the  other  cases  in  which  such  optima  occur 
(cf.  p.  53). 

Reichel  and  Spiro2  have  contributed  some  interesting 

1  Fuld  :  Hofmeisters  Beitr'dge,  2.  169  (1902). 

2  Reichel  and  Spiro  :  Hofmeisters  Beitrage,  7.  478  (1905). 


74 


LECTURES  ON   IMMUNITY 


figures  regarding  the  coagulation  of  milk  at  different 
dilutions  or  with  the  addition  of  different  quantities  of 
calcium  chloride.  The  most  interpretable  results  were 
yielded  by  the  additions  of  calcium  chloride.  The  milk 
itself  contained  0.6  per  cent  if  diluted  in  the  proportion 
10 :  8,  which  was  employed  in  these  experiments.  Eight 
c.c.  of  milk  were  mixed  with  i,  0.5,  or  0.25  c.c.  of  a  rennet 
solution,  R,  and  with  different  amounts  of  a  solution  of 
calcium  chloride  and  water  until  the  total  volume  was 
10  c.c.  The  authors  give  the  following  values:  — 


CACLj  IN  % 

TIME  OF  COAGULATION 

CONSTANT=  (/  +  0.6)  t 

* 

i  c.c.  X 

0.5  c.c.  R 

0.25  c.c.  R 

i  c.c.  R 

0.5  c.c.  R 

0.25  c.c.  R 

0 

95 

48 

24 

57 

28.8 

14.4 

0.05 

88.6 

45.6 

23 

57.6 

29.6 

15.0 

O.I 

79 

41.6 

22 

55-3 

29.1 

15-4 

0.2 

66.4 

36 

19 

53-1 

28.8 

15.2 

0-5 

48 

26.4 

H 

52.8 

29.0 

15-4 

1.0 

30 

1  8.2 

10.6 

48.0 

29.1 

17.0 

2.O 

17 

II 

6.8 

44.2 

28.6 

17.7 

5-o 

10 

7-4 

5-4 

56.0 

41.4 

30.2 

10.0 

13 

9.2 

6.2 

137-8 

97-5 

65.7 

20.0 

22 

15 

8.6 

453-2 

309 

177.2 

As  will  be  seen  from  these  figures,  the  product 
(/  +  o.6y  is  nearly  constant,  if  p  does  not  exceed  2%. 
This  relation  is  quite  like  that  representing  the  connection 
between  the  quantity  of  rennet  and  time  of  coagulation. 
If  the  quantity  of  rennet  is  called  R,  the  complete  equa- 
tion for  the  time  of  action  is  R(p  4-  o.6)/  =  const.  The 
value  0.6  which  must  be  added  to  p  to  obtain  a  constant 
value  may  be  regarded  as  the  quantity  of  calcium  ions 


VELOCITY  OF  REACTION.     HOMOGENEOUS  SYSTEMS       75 


present  if  no  calcium  chloride  is  added.1  Chlorides  of 
barium  and  magnesium  exert  a  similar  influence  to  that 
of  calcium ;  the  less  ionised  magnesium  sulphate  has  an 
analogous  but  weaker  action. 

In  another  series  of  experiments  the  concentration  of 
the  casein  was  changed.  The  solvent  by  means  of  which 
the  attenuation  was  accomplished  was  milk  freed  of  casein, 
i.e.  whey.  The  experimental  values  are  given  below  ;  the 
quantity  of  rennet  present  was  always  the  same,  I  c.c.  of  a 
given  solution. 


MILK 

WHEY 

TIME  OF  COAGULATION 

obs. 

calc. 

c.c. 

c.c. 

sec. 

sec. 

0.2 

8.8 

no 

no 

0.4 

8.6 

70 

64 

0.6 

8.4 

50 

49 

0.8 

8.2 

42 

42 

I.O 

8.0 

39 

374 

1.25 

7-75 

33 

33-8 

i-5 

7-5 

31-2 

31.5 

'•75 

7-25 

29.6 

29.9 

2 

7 

28.6 

28.6 

2.5 

6-5 

27 

26.8 

3 

6 

26 

257 

4 

5 

24 

23.2 

5-5 

3-5 

23 

23.0 

8 

i 

22 

21.8 

The  calculated  values  for  the  time  of   coagulation  (/) 
are  found  by  means  of  the  empirical  formula  :  — 

10  —  M 


t—  21.6=  1.75- 


M 


1  As  the  authors  assert,  this  supposition  assumes  that  only  about  15  per 
cent  of  the  calcium  salts  present  in  milk  are  in  ionic  state. 


f6  LECTURES  ON   IMMUNITY 

where  M  denotes  the  quantity  of   milk  (in  cubic  centi- 
meters) present  in  the  solution. 

Very  complicated  results  were  obtained  on  dilution  with 
0.9  per  cent  solution  of  sodium  chloride,  as  is  seen  from 
the  following  table,  in  which  M  and  R  respectively  desig- 
nate the  number  of  cubic  centimeters  of  milk  and  rennet 
respectively  present  in  10  c.c.  of  the  solution.  (The 
rennet  contained  calcium  salts.)  The  rest  (10  —  M—  R  ) 
is  the  quantity  of  salt  solution  added.  The  tabulated 
figures  give  the  time  of  coagulation  in  seconds. 

R  =  2    1.5  i  0.9       0.8  0.7  0.6  0.5  0.4  0.3 

M=  1.25  c.c.  34  9  12  14.5  19  33  50  107  810 

3      c.c.  46  10  11.5  '14  18  24  32  45  78 

8      c.c.  8    9  ii  12          14  16  19  23  29  42 

If  R  =  0.8  or  0.9  c.c.,  the  time  of  coagulation  is  nearly 
independent  of  the  dilution  of  the  milk ;  at  lower  concen- 
trations of  R  the  time  increases  with  dilution,  at  higher 
concentrations  of  R  the  opposite  is  true. 

According  to  the  views  of  Saw]  alow  the  coagulation  of 
milk  is  only  a  special  case  of  digestion  in  which  one  of  the 
products  coagulates.  This  agrees  very  well  with  experi- 
ments at  low  temperatures  first  executed  by  Morgenroth,1 
and  then  repeated  by  Fuld.  They  prepared  mixtures  of 
rennet  and  milk,  which  were  held  at  low  temperatures. 
Then  no  coagulation  occurred,  but  the  digestion  process  did 
occur.  After  these  mixtures  had  been  held  for  some  time 
at  the  low  temperature  and  were  then  heated  to  20°  or 
more,  they  coagulated  instantaneously. 

1  Morgenroth :  Archives  Internationales  de  pharmarcodynamie,  7.  265 
(1900). 


VELOCITY  OF   REACTION.      HOMOGENEOUS  SYSTEMS       77 

As  we  have  seen  above,  the  albumose-salts  produced  in 
the  digestion  exert  an  enormous  retarding  influence  on 
the  velocity  of  digestion.  In  the  same  manner  according 
to  Sawjalow  the  addition  of  peptone  to  a  mixture  of  milk 
and  gastric  juice  increased  the  time  of  coagulation  to  a 
notable  degree.  This  time,  for  instance,  increased  from 
29.8  seconds  to  791  seconds  on  the  addition  of  4  c.c.  of 
peptone  solution  (i  c.c.  was  equivalent  to  5.5  mg.  HC1) 
instead  of  4  c.c.  of  water  to  a  mixture  of  i  c.c.  stomachal 
fluid  with  10  c.c.  of  milk.  The  action  was  therefore  dimin- 
ished to  about  4  per  cent.  A  like  influence  is  exerted  by 
peptone  solution  on  the  velocity  of  reaction  on  milk  of 
pancreatic  juice  or  of  solution  of  papayotin. 

As  peptone  is  very  nearly  related  to  albumose,  this 
seems  to  indicate  that  the  digestive  action  of  pepsin  is 
identical  with  the  coagulating  influence  of  rennet  or  pan- 
creatic liquid  or  papayotin,  as  Pawlow  and  Sawjalow  have 
contended.  A  substance  that  acts  in  a  similar  manner  to 
pepsin  on  thymolgelatin  is  trypsin.  On  the  action  of  dif- 
ferent quantities  (from  0.0022  to  0.3  c.c.)  at  47.3°  C.  the 
following  investigations  were  carried  out  by  Madsen  and 
Walbum.  In  this  case  no  acid  was  added  to  the  liquid  in 
the  test-tubes,  but  only  2  c.c.  of  thymolgelatin,  q  c.c.  of 
trypsin  solution,  and  (2  —  q)  c.c.  of  I  per  cent  salt  solution. 
These  investigations  indicate  that  in  this  case,  as  well  as  in 
those  treated  above,  the  product  of  the  time  of  reaction 
and  reacting  quantity  is  a  constant,  if  the  magnitude  of 
reaction  is  the  same.  In  the  following  table  the  signs  / 
and  q  denote  time  and  quantity:  — 


78  LECTURES  ON  IMMUNITY 

LIQUEFACTION  OF  THYMOLGELATIN  BY  MEANS  OF  TRYPSIN  AT  47.3°  C. 


9 

t  (hours) 

qt 

9 

/  (hours) 

ft 

0-3 

0.16 

0.048 

0.0072 

8 

0.058 

0.105 

o-5 

0.052 

0.006 

IO 

0.060 

0.05 

i 

0.050 

0.0037 

16 

0.059 

0.027 

2 

0.054 

O.OO32 

18 

0.058 

0.02 

3 

0.06 

0.0027 

20 

0.054 

0.015 

4 

0.06 

0.0025 

22 

o-°55 

O.OII 

5 

o-055 

0.0022 

24 

o-o53 

O.OO9 

6 

0.054 

Mean    0.056 

With  another  preparation  of  trypsin  the  effect  of  tem- 
perature was  studied.  The  inverse  value  of  qt  may  be 
regarded  as  the  constant  of  reaction ;  it  was  found  to  have 
the  following  values  :  — 


=  -,    /*=  10,5/0. 


INFLUENCE  OF  TEMPERATURE  ON  THE  DIGESTION  OF  GELATIN  BY  MEANS 

OF  TRYPSIN 


TEMP. 

*+, 

*•«*. 

22.6 

4.18 

4.04 

24-75 

444 

4.60 

29.2 

5.72 

5-98 

36.5 

9.01 

9.06 

39-8 

10.89 

10.85 

44.96 

14.52 

14.30 

50.2 

18.35 

18.74 

In  most  of  the  series  of  Madsen  and  Walbum  an  in- 
crease of  qt  with  time  is  observed.  This  may  be  explained 
by  the  binding  of  a  little  of  the  trypsin  or  by  the  weaken- 
ing of  it  with  time,  p  is  nearly  the  same  as  for  pepsin. 


VELOCITY  OF  REACTION.      HOMOGENEOUS   SYSTEMS       79 

Bayliss  1  has  investigated  the  progress  of  the  action  of 
trypsin  on  casein  by  means  of  the  method  of  Sjb'qvist.  A 
solution  of  8  per  cent  of  the  sodium  salt  of  casein  was  pre- 
pared and  to  6  c.c.  of  this  solution  2  c.c.  of  0.5  normal 
ammonia  and  2  c.c.  of  a  2  per  cent  solution  of  trypsin  were 
added.  The  conductivity  was  measured  at  different  times 
and  its  increase  (at  39°  C.)  plotted  in  a  curve.  This  curve 
tends  to  an  upper  limit.  By  measuring  the  ordinates  (  Y) 
in  millimeters  of  this  curve  I  have  found  the  following 
values  :  — 


PROGRESS  OF  DIGESTION  OF  CASEIN 
WITH  TRYPSIN  AT  39°  C. 

PROGRESS  OF  DIGESTION    OF    EGG- 
WHITE  BY  TRYPSIN  AT  39°  C. 

TIME  (hours) 

**. 

n*ie. 

TIME  (hours) 

*•*.. 

*".*. 

0-3 

25.0 

29.0 

I 

10.2 

10.2 

o-5 

35-5 

35-7 

2 

15.0 

13-8 

0.7 

41.0 

40.8 

4 

18.8 

I8.5 

I.O 

48.0 

46.4 

6 

22.0 

22.0 

i-S 

55-5 

53-7 

8 

24.0 

24.1 

2.O 

59-2 

584 

10 

25.5 

26.5 

2-5 

62.2 

61.4 

'5 

29.2 

30.3 

3-0 

64.6 

64.2 

20 

3L8 

33-2 

3-5 

66.0 

66.4 

25 

33-6 

35-3 

4 

67.5 

68.1 

30 

354 

36.9 

5 

70.0 

70.8 

40 

38 

394 

6 

71.4 

72.6 

5° 

4i 

41 

7 

72.7 

73-3 

00 

45 

— 

8 

74.2 

74.8 

oo 

(77-0) 

— 

The  calculated  values  are  found  with  the   aid  of  the 
formula  KP  =  320,  adopted  for  the  pepsin  action.     They 


1  Bayliss :  Archives  des  sciences  biologiques,  II.  Suppl.  p.  261,  St.  Peters- 
burg, 1904. 


80  LECTURES  ON  IMMUNITY 

agree  very  closely  with  the  observed  ones.  The  same  is 
the  case  for  the  digestion  of  the  solution  of  egg-white, 
which  had  been  previously  heated  to  100°  C.  in  order  to 
destroy  its  content  of  antitrypsin.  The  solution  contained 
10  c.c.  of  a  mixture  of  10  per  cent  of  egg-white  and  90  per 
cent  of  distilled  water,  and  further  i  c.c.  of  a  i  per  cent 
solution  of  trypsin.  Here  KP  =  30.  The  reaction  with 
casein  increases  (the  determination  is  not  very  reliable) 
in  the  proportion  i  :  5.3  between  20.7°  and  30.7°  C. 
0  =  29,500)  and  1:2.6  between  30.7°  and  38.7°  and  has 
probably  an  optimum,  due  to  the  instability  of  trypsin  at 
higher  temperature. 

In  this  case  the  increase  of  conductivity  depends  prob- 
ably on  the  formation  of  ammonium  salts  of  the  reaction- 
products.  These  also  react  with  the  trypsin,  so  that  the 
quantity  of  free  trypsin  is  nearly  inversely  proportional  to 
the  quantity  of  reaction-products,  whereby  the  reaction 
progresses  proportionally  to  the  square  root  of  the  time 
in  its  first  period.  Bayliss  showed  that  the  addition  of 
digestion-products,  as  well  as  asparagin,  glycin  (Merck), 
leucin,  and  amphopepton  (Griibler),  retards  the  action  of 
trypsin  to  a  high  degree. 

Henri  and  Larguier  de  Bancels l  have  used  the  method 
of  Sjoqvist  for  the  study  of  digestion  by  pancreatic  juice. 
They  found  that  this  process  of  tryptic  digestion  follows 
the  laws  for  monomolecular  reactions  and  give  as  an  illus- 
tration the  following  figures  for  the  changes  in  the 
conductivity  with  time  (at  44°,  4  per  cent  solution  of 
gelatine). 

1  Victor  Henri  and  Larguier  de  Bancels  :  C.  JR.  de  ta  Soc.  de  Biol.  55. 
787,  789,  and  866  (1903). 


VELOCITY  OF  REACTION.     HOMOGENEOUS   SYSTEMS       8 1 


TIME  (min.) 

CHANGE  OF  CONDUCTIVITY 

MEAN 

7-37  *t 

IO 

27 

28 

27 

27-3 

29-3 

2O 

46 

44 

42 

44 

41-5 

30 

53 

55 

5i 

53 

50.0 

40 

58 

60 

58 

58.7 

58.7 

55 

66 

66 

65 

65.7 

68.8 

As  the  end-value  was  not  measured,  we  may  only  con- 
clude that  the  change  of  the  conductivity  is  very  nearly 
proportional  to  the  square  root  of  the  time  of  digestion,  as 
is  seen  in  the  last  column.  It  might  therefore  be  regarded 
as  probable  that  these  experiments  are  not  in  opposition 
with  those  made  by  other  observers,  who  have  found  that 
the  rule  of  Schutz1  holds  good  during  the  first  time  of 
digestion.  The  same  authors  have  also  digested  casein  dis- 
solved in  a  2  per  cent  solution  of  sodium  carbonate  in  the 
same  manner.  They  found  the  following  changes  of  the 
conductivity  (at  44°  C.)  :  — 


TIME 

CHANGE 

5-59  V* 

10 

24 

24 

20 

36 

34 

30 

41 

42 

40 

42 

48 

50 

44 

54 

During  the  first  time  (30  min.)  the  change  is  nearly  pro- 
portional to  the  square  root  of  the  time. 

Another  series  of  experiments  were  concerned  with  the 
problem  of  the  digestion  of  different  quantities  of  gelatine 
or  casein,  or  of  both  simultaneously,  by  means  of  a  con- 


1  Schiitz  and  Huppert  :  Pfluger*s  Archiv.  80.  470  (1900). 
G 


82 


LECTURES  ON  IMMUNITY 


stant  quantity  of  trypsins.     The  results  are  given  below 
together  with  some  calculated  figures :  — 


TIME 

G.  3-5  % 

G.i.75% 

C.2.5% 

C.  1.25% 

obs.          calc. 

obs.         calc. 

obs.           calc. 

obs.         calc. 

10 

17         18 

II            13 

23              26 

20           18 

20 

30           25 

18          18 

39          37 

26           26 

30 

37         29 

20            22 

46          45 

28           32 

G.  3-5%-!-  C.  2.5% 

G.3.s%+  C.i.  25% 

G.  1.75%  +  C.  2.5% 

G.  1.75  %+C.  1.25% 

obs.              calc. 

obs.              calc. 

obs.              calc. 

obs.             calc. 

25                 32 

28                24 

25                29 

28               22 

50            45 

45             34 

47            4i 

42               32 

63            55 

55            4i 

58            50 

47           39 

The  calculated  values  a*re  obtained  on  the  basis  of  the 
assumption  that  the  digested  quantities  for  the  gelatin 
are  proportional  to  3.05^-  A  and  for  the  casein  to 
5.2  V^A  where  c  is  the  concentration  of  per  cent  and  t  the 
time  in  minutes.  (In  the  table  above  G  represents  gelatin 
and  C  represents  casein.)  The  agreement  seems  to  be 
within  the  errors  of  observation,  so  that  we  may  well  con- 
clude that  the  mass  digested  is,  for  short  times,  propor- 
tional to  the  square  root  of  the  concentration  as  well  as  of 
the  time.  The  calculated  values  for  the  mixtures  are 
made  under  the  assumption  that  I  per  cent  of  casein 
is,  so  to  speak,  equivalent  to  2.9  per  cent  of  gelatin 


2.9 


Therefore  3.5  per  cent  gelatin  +  2.5  per 


cent  casein  are  equivalent  to  3.5  -f  7.3  =  10.8  per  cent 
gelatin.  The  observed  effect  is  in  most  cases  greater 
than  the  calculated  one  for  the  mixtures  ;  only  for  a  brief 
period  do  they  correspond  closely.  It  therefore  seems 


VELOCITY   OF  REACTION.      HOMOGENEOUS   SYSTEMS       83 

probable  that  the  rule  for  this  calculation  agrees  well  with 
the  facts  only  for  short  times ;  a  closer  examination  of  this 
circumstance  can  be  done  only  when  we  know  the  limit 
values  of  the  change  of  conductivity,  and  even  then  new 
observations  ought  to  be  carried  out  and  multiplied. 

The  above  calculation  is  carried  through  on  the  assump- 
tion that  the  products  of  digestion  from  casein  exert  the 
same  binding  influence  on  the  reacting  bodies  (probably 
the  trypsin)  as  do  the  corresponding  derivatives  from  gela- 
tin, since  they  cause  the  same  change  of  the  conductivity. 
This,  of  course,  need  not  necessarily  be  the  case;  it  is 
only  the  simplest  hypothesis  we  may  introduce  in  the 
present  undeveloped  state  of  research  on  this  point. 
Hence  it  is  not  necessary  at  all  to  suppose  that  the  trypsin 
is  bound  by  the  gelatin  and  the  casein  to  explain  that  the 
observed  effect  on  digesting  gelatin  and  casein  simultane- 
ously is  less  than  the  sum  of  the  effects  of  the  digestion 
of  the  two  substances  separately,  as  Henri  and  Larguier 
suppose.  Their  hypothesis  might  be  well  founded,  if  we 
could  observe  the  digestion  in  such  an  early  period  where 
the  quantity  digested  was  proportional  to  time,  or,  in 
other  words,  when  the  products  of  digestion  would  be 
much  inferior  in  quantity  (according  to  equivalents)  to 
the  quantity  of  trypsin.  But  this  condition  is  not  ful- 
filled in  these  or  in  any  other  experiments  on  tryptic 
digestion. 

With  the  use  of  a  different  substratum,  however,  the 
action  of  trypsin  exhibits  a  different  behaviour.  As  deter- 
mined by  Taylor,1  when  protamin  is  digested  by  trypsin, 
the  acceleration  produced  by  the  ferment  is  directly  pro- 

1  Taylor,  University  of  California  Publications,  Pathology,  I,  21,  1904. 


84 


LECTURES  ON  IMMUNITY 


portional  to  its  mass.     This  has  been  confirmed  by  Euler,1 
who  digested  glycyl-glycin  by  means  of  trypsin. 

Henri  and  Lalou2  have  also  carried  out  some  measure- 
ments on  the  decomposition  of  amygdalin  and  salicin  by 
means  of  emulsin  at  26°  C.  The  readings  were  deter- 
mined by  means  of  a  polarimeter.  An  example  may  be 
given :  — 


TIME  (min.) 

SALICIN  a  % 

AMYGDALYN 

z.5% 

SALICIN  2  %  + 
AMYGDALIN  2.5% 

SALICIN  4  % 

AMYGDALIN  1.25% 

46 

0.67 

0.97 

1.05 

1.  08 

0.90 

130 

I.58 

2.38 

3-63 

2.25 

i-57 

268 

2.32 

3.15 

4.22 

345 

1.56 

00 

3-15 

3.17 

6.32 

6.30 

1.59 

The  decomposition  of  the  mixture  is  much  slower  than 
the  sum  of  the  decompositions  of  the  constituents.  For 
comparison  the  rates  of  decomposition  of  4  per  cent  salicin 
and  of  1.25  per  cent  amygdalin  under  similar  conditions 
are  given  in  parallel.  The  explanation  of  the  difference 
is  evidently  the  same  as  that  of  the  non-proportionality  of 
reaction  and  concentration,  but  it  offers  no  more  stringent 
conclusions,  regarding  the  combination  of  enzyme  and  sub- 
strate, than  does  this  latter  circumstance. 

Weis3  has  carried  out  a  great  number  of  experiments  on 
the  digestion  of  the  protein  from  wheat  by  means  of  tryp- 
sin or  pepsin  (extract  of  malt).  A  great  interest  is  attached 
to  those  experiments  in  which  the  quantity  of  protein  was 
varied.  In  the  experiments  on  digestion  cited  above,  the 

3  Euler:  Arkiv  fur  Kemi,  2.  No.  31,  p.  8,  Stockholm,  1907. 
2  Henri  and  Lalou  :  C.  R.  de  la  Soc.  de  Biol.  55.  868  (1903). 
8  Fr.  Weis  :  Meddelelser  fra  Carhbtrg-Laboratorict,  5.  127  (1903)- 


VELOCITY  OF  REACTION.     HOMOGENEOUS  SYSTEMS       85 


protein  was  always  present  in  constant  amount.  In  the 
following  table  the  quantity  of  protein  is  given  in  per  cent 
n  of  the  total  liquid  examined.  After  this,  is  tabulated  the 
quantity  of  protein,  in  per  cent  of  the  whole  quantity,  which 
had  been  digested  in  2  or  in  5  hours.  If,  for  instance, 
the  digested  quantity  is  10  per  cent  of  the  original  quantity 
of  protein,  the  total  quantity  of  digestion-products  is  double 
as  great  if  «  =  2,  as  if  n=  i.  Now  the  velocity  of  reac- 
tion is  inversely  proportional  to  the  quantity  of  digestion- 
products,  therefore  the  point  where  10  per  cent  are  digested 
is  reached  later  if  ;z=2,  than  if  n—\.  The  digested 
quantity  is  therefore  nearly  inversely  proportional  to  the 
square  root  of  n,  as  is  seen  from  the  following  figures, 
which  are  compared  with  figures  calculated  from  the  gen- 
eral formula  on  p.  64  :  — 


n 
(per  cent) 

DIGESTED  QUANTITY  AFTER 

a  HOURS 

5  HOURS 

obs. 

calc. 

obs. 

calc. 

I 

22.0 

21.4 

36.2 

32.4 

2 

17.0 

I5.6 

25-9 

23.8 

3 

I3.I 

12.9 

20.3 

19.8 

4 

9-i 

II.  2 

1  6.0 

17-3 

5 

7-9 

1  0.0 

13-2 

I5.6 

The  agreement  seems  to  be  satisfying  considering  the 
rather  complex  composition  of  the  substrate.  It  indicates 
that  the  quantity  of  digestible  matter  enters  in  the  formula 
in  the  same  manner  as  the  quantity  of  enzyme.  In  all 
cases  of  digestion  or  lipolysis  which  are  subject  to  the 
formulae  given  above,  p.  64,  that  is  to  Schiitz's  rule,  if  the 
process  has  not  gone  too  far,  the  concentration  of  the  sub- 


86 


LECTURES  ON  IMMUNITY 


strate  plays  the  same  role  as  that  of  the  enzyme  or  as  the 
time,  which  is  also  probable  on  the  theoretical  grounds. 
The  products  from  a  culture  of  Bacillus  pyocyaneus 
exert  a  liquefying  action  on  thymolgelatin,  just  as  do  pep- 
sin or  trypsin.  This  action  was  investigated  by  Madsen 
and  Walbum.  It  was  found,  as  for  pepsin  and  trypsin, 
that  the  time  necessary  for  liquefying  the  gelatin  to  the 
stated  degree  is  inversely  proportional  to  the  quantity  of  cul- 
ture employed.  The  bouillon  in  which  the  B.  pyocyaneus 
had  been  cultivated  for  two  weeks  was  filtered  through  a 
Chamberland  filter  and  a  certain  quantity  (q  c.c.)  added  to 
2  c.c.  of  7  per  cent  thymolgelatin  and  (2  —  q)  c.c.  of  i  per 
cent  NaCl  solution.  The  experiments  were  done  at  34.5°  C. 
DIGESTION  OF  THYMOLGELATIN  BY  MEANS  OF  PYOCYANEUS  CULTURE 


f 

TIME  t  (hours) 

it 

9 

TIME  t  (hours) 

9' 

1.6 

0-5 

0.8 

O.I  I 

8 

0.88 

0.8 

I 

0.8 

0.09 

10 

0.90 

0.46 

2 

0.92 

0.08 

12 

0.96 

0-3 

3 

0.9 

0.06 

I6.5 

0.99 

0.22 

4 

0.88 

0.044 

18 

0.79 

0.2 

4-5 

0.9 

0.042 

20 

0.84 

O.I7 

6 

1.02 

0.035 

25 

0.88 

Mean  0.89 

Madsen  and  Walbum  have  investigated  the  destruction 
of  coli-agglutinin  by  means  of  trypsin  at  35. 6° C.  The 
strength  of  the  agglutinin  was  determined  by  means  of  its 
agglutinating  power.  The  observed  quantity,  q,  is  that 
quantity  of  agglutinin  which  must  be  added  to  a  sus- 
pension of  Bacillus  coli  to  obtain  a  given  agglutination 
in  a  given  time.  These  values  are  tabulated  below.  The 
strength  5  is  the  inverse  value  of  q.  The  reaction  is 


VELOCITY   OF   REACTION.      HOMOGENEOUS   SYSTEMS       8/ 


calculated    according    to    the    formula    for    bimolecular 
reactions.     K=6S.io~5. 

DESTRUCTION  OF  i  c.c.  OF  COLI-AGGLUTININ  SOLUTION  BY  MEANS  OF  5  c.c. 
OF  i%  SOLUTION  OF  TRYPSIN  AT  37.5° 


TIME  (hours) 

•Sobs. 

•Scale. 

TIME  (hours) 

•Sobs. 

•Scale. 

0 

1000 

1000 

6 

I89 

197 

o-5 

775 

763 

8 

I49 

155 

i 

610 

600 

10 

I40 

128 

2.25 

389 

395 

12 

108 

I09 

3 

280 

329 

14 

88 

95 

4.17 

259 

261 

23 

61 

57 

5 

233 

227 

25 

59 

56 

The  agreement  is  very  satisfactory  at  the  beginning, 
if  we  consider  that  the  errors  of  observation  are  rather 
large.  This  method  gives  a  direct  determination  of  the 
destruction,  and  not  an  indirect  one,  as  do  the  measure- 
ments of  the  electrical  conductivity. 

The  destruction  of  rennet  increases  very  rapidly  with 
increasing  temperature,  as  is  shown  by  the  following  table  : 


WEAKENING  OF  RENNET  IN  2  % 
SOLUTION  AT  47.55  °  C. 


WEAKENING  OF  RENNET  (2  %  SOL.) 
AT  DIFF.  TEMPERATURES 


/  (min.) 

•Sobs. 

•Scale. 

TEMP. 

-^obs. 

•A"calc. 

0 

20 

17.9 

44-51 

O.OI27 

O.OII 

2-5 

14-3 

14-3 

46.04 

0.0231 

0.022 

5 

10.5 

II.4 

47-55 

0.039 

0.0414 

7-5 

8-3 

9.1 

48.57 

0.0646 

0.0647 

10 

7-i 

7-i 

49.12 

0.072 

0.0836 

12.5 

5-9 

5-9 

49.6 

O.IOI 

O.I  O2 

15 

5-o 

4.8 

17.5 

4.0 

3-7 

20 

3-0 

3-0 

22.5 

2.2 

2.2 

25 

1.8 

1.9 

K  =  0.0386. 


/*  =  89,130. 


88 


LECTURES  ON  IMMUNITY 


The  reaction  is  monomolecular.  The  influence  of  tem- 
perature is  characterised  by  a  rather  high  value  of  /*. 
A  second  series  gave  /*  =  91,000,  so  that  in  the  mean 
/A  =  90,000.  This  attenuation  is  much  more  marked  in 
weaker  than  in  stronger  concentrations,  as  is  indicated  by 
the  following  figures,  valid  for  the  temperature  46.i5°C.: 


CONCENTRATION 

VELOCITY  OF  DESTRUCTION 

CONCENTRATION 

VELOCITY  OF  DESTRUCTION 

7 

0.00372 

I 

0.028 

6 

0.003 

°-5 

0.032 

5 

0.0049 

0.25 

0.039 

4 

0.0077 

0.125 

O.o6o 

3 

0.0154 

0.0625 

0.073 

2 

O.O2I2 

Dried  powder  of  rennet  is  very  resisting  to  the  influence 
of  temperature ;  ^=0.0414  at  I58°C.  The  reaction  was 
monomolecular. 

The  destruction  of  the  rennet  is  to  a  high  degree  accel- 
erated by  the  presence  of  an  alkali.  To  200  c.c.  of  a  10 
per  cent  rennet  solution  Madsen  added  from  0.5  c.c.  to  3  c.c. 
of  i  n.  NaOH.  He  found  that  the  velocity  of  destruction 
proceeds  more  slowly  than  that  of  a  monomolecular  re- 
action. This  circumstance  is  probably  due  to  a  retarding 
influence  of  the  reaction-products.  This  influence  may  in 
the  following  example,  in  which  3  c.c.  of  i  n.  NaOH 
acted  upon  200  c.c.  of  a  solution  of  rennet  at  46°  C,  be 
put  proportional  to  the  third  root  of  the  quantity  of  ren- 
net. ^Ob8  indicates  the  quantity  of  rennet  which  is  neces- 
sary to  cause  coagulation  in  ten  minutes.  q^Cf  is  the 
corresponding  calculated  quantity. 


VELOCITY  OF  REACTION.     HOMOGENEOUS  SYSTEMS       89 


DESTRUCTION  OF  RENNET  IN  PRESENCE  OF  SODIUM  HYDRATE  AT  46°  C. 


/  (min.) 

fobs. 

^calc. 

/  (min.) 

^obs. 

^calc. 

0 

0.040 

O.O4O 

10 

0.50 

0.48 

2 

0.073 

0.079 

12 

0.70 

0.66 

4 

0.130 

0.139 

14 

1.  00 

0.88 

6 

0.20 

O.22 

16 

1-15 

«•«$ 

8 

0-35 

0-33 

The  calculated  values  are  deduced  from  the  formula: — 
fi*  -?o*  =0,044  ('i-'o). 

Madsen  has  also  investigated  the  destruction  of  trypsin 
by  means  of  alkalies  and  found  similar  regularities  as  for 
the  destruction  of  pepsin. 

Regarding  the  spontaneous  attenuation  of  pepsin,  Mad- 
sen  and  Walbum  found  that  the  reaction  is  monomolecular, 
which  is  shown  in  the  following  table.  The  increase  of 
this  reaction  with  temperature  gives  /*= 75,600,  that  is,  |  of 
the  value  for  rennet  (2  per  cent  solution).  As  the  prepa- 
rations are  not  identical  and  even  used  in  different  concen- 
trations, this  difference  does  not  afford  any  data  bearing  on 
the  possible  identity  of  rennet  and  pepsin.  The  strength  of 
the  pepsin  was  determined  by  means  of  its  digesting 
influence  on  thymolgelatin. 


WEAKENING  OF  PEPSIN   (5%   SOL.) 
AT  66.8° 


WEAKENING  OF  PEPSIN  AT  DIFFERENT 
TEMPERATURES 


t  (min.) 

STRENGTHobg 

STRENGTHcalCi 

TEMP. 

•^obf. 

•*"calc. 

0 

17-5 

I7.6 

57 

O.OOII2 

O.OOII2 

5 

II.  I 

12.8 

60 

0.0047 

0.0036 

10 

8-33 

8.71 

63.3 

0.0109 

0.0098 

20 

4-35 

4.34 

64.8 

O.OI4I 

0.0160 

30 

2.22 

2.25 

66.8 

0.0305 

0.0305 

40 

I.  II 

1.06 

0.0305. 


=  75,600. 


LECTURES  ON   IMMUNITY 


Trypsin  behaves  in  a  manner  very  similar  to  that  of 
rennet  and  pepsin.  The  reaction  of  the  spontaneous 
attenuation  is  monomolecular  and  the  velocity  constant 
of  reaction  increases  very  rapidly  with  temperature 
(//.  =  62,000).  The  values  are  given  below:  — 


DESTRUCTION  OF  TRYPSIN  AT  64.03°  C. 

DESTRUCTION  OF  TRYPSIN  AT  DIFFER- 
ENT TEMPERATURES 

t  (min.) 

STRENGTHobg 

STRENGTHcajc 

TEMP. 

^oba. 

/ircalc. 

O 

12.5 

I2.I 

60.72 

0.00127 

0.00127 

5 

1  1.8 

11.6 

61.95 

O.OOlS 

O.OOlS 

ii 

u.  i 

ii.  i 

63 

O.OO24 

0.0024 

15 

10.5 

10.8 

64.03 

O.OO32 

0.0032 

20 

1  0.0 

10.4 

67.15 

0.0073 

0.0074 

30 

9.1 

9.6  > 

72.15 

0.0274 

0.0274 

40 

8.7 

9.0 

74-35 

0.049 

0.049 

50 

8-3 

8-3 

60 

7-7 

7-7 

80 

6.7 

6.7 

IOO 

5-9 

5-9 

120 

5.6 

5-0 

K  =  0.0031 7.  (j.  =  62,034. 

The  concentration  of  the  trypsin  solution  exerts  no 
sensible  influence  on  the  rate  of  destruction  in  this  case. 
Solutions  containing  2,  4,  6,  8,  or  10  per  cent  of  trypsin 
all  gave  satisfying  results  when  calculated  with  the 
value  K=  0.0073  (at  67.15°  C).  The  strength  of  the 
trypsin  was  measured  by  means  of  its  property  of  liquefy- 
ing thymolgelatin. 

Trypsin  exerts,  as  we  saw,  a  destructive  influence  on 
coli-agglutinin,  and  this  destruction  proceeds  faster  at 
higher  temperature  than  at  lower,  as  is  seen  from  the 
following  measurements  of  Madsen  and  Walbum.  At 
44.2°  C.  the  calculated  values  differ  for  some  time  rather 


VELOCITY  OF  REACTION.      HOMOGENEOUS   SYSTEMS       91 


widely  from  the  observed  ones,  probably  because  of  the 
spontaneous  destruction  of  the  trypsin. 

DESTRUCTION  OF  COLI-AGGLUTININ  (i  c.c.)  BY  TRYPSIN  (5  c.c.  i  %  SOL.) 
AT  DIFFERENT  TEMPERATURES 


AT  33-5°  C. 

AT  37.2°  C. 

AT  44.  2°  C. 

TIME 

(hours) 

Strength 

Strength 

Strength 

fobs. 

obs.           rale. 

?obs. 

obi.          calc. 

?obs. 

obg.        calc. 

O 

0.00  1 

1000 

IOOO 

0.00  1 

IOOO 

IOOO 

0.00  1 

IOOO 

IOOO 

1-25 

0.0017 

539 

602 

0.002 

S00 

515 

0.0025 

400 

407 

3 

0.0023 

435 

386 

0.0027 

370 

308 

0.005 

200 

222 

5 

0.0038 

263 

274 

0.0047 

213 

211 

0.008 

"5 

146 

8 

0.005 

200 

191 

0.008 

125 

141 

0.0095 

I°5 

96 

12 

0.008 

125 

136 

O.OI 

100 

100 

O.OII5 

87 

66 

10*^=53 

lo5  K  =  75  (calc.  70) 

id^IC—  117 

u  =  14200 

The  method  used  for  measuring  the  potency,  i.e.  the 
inverse  value  of  the  quantity  ^Ob8  necessary  for  the  pro- 
duction of  a  certain  degree  of  agglutination,  is  that 
described  by  Madsen  and  Jorgensen.1  From  the  observa- 
tions the  values  K  are  calculated,  by  means  of  which  the 
calculated  values  for  the  potency  are  deduced  according 
to  the  formula  for  bimolecular  reactions.  The  agreement 
with  the  observed  values  is  satisfactory.  From  the  two 
values  at  33.5°  and  44.2°  C.  the  value  p=  14,200  is  calcu- 
lated by  means  of  the  general  formula.  With  this  value 
of  fM  we  find  1 0^=70  at  37.2°  C.  in  satisfactory  agree- 
ment with  the  observed  value  75. 

A  peculiar  regularity  is  found  for  the  coagulating  power 
of  fibrin  ferment  on  plasma.  Here  the  product  of  time 
of  reaction  and  concentration  is  not  nearly  constant,  as 
in  the  coagulation  of  milk  by  rennet,  but  the  product  of 

1  Fcstskriftvtdlndvidscn  afStatcns  Serum  Institut,  Copenhagen,  1902,  No.  5. 


LECTURES  ON   IMMUNITY 


the  concentration  to  the  power  f  and  time  of  reaction 
gives  a  nearly  constant  value,  as  indicated  by  the  figures 
below,  found  by  Madsen  and  Walbum,  as  well  as  by  Fuld  :l 


PLASMA  AND  MUSCLE  EXTRACT  FROM  HORSE 
(MADSEN  AND  WALBUM  2) 

BLOOD  PLASMA  OF  GOOSE  (2 
c.c.)  WITH  6  c.c.  OF  EXTRACT 
OF  GOOSE  MUSCLE  (FULD) 

/  (min.) 

c 

*(io  C)1 

/=TlME 

(min.) 

CONC. 

(O 

tc\ 

c 

£=TlME 

(seconds) 

/x(io  Of 

105 

0.6 

330 

80 

2 

127 

0.2 

80 

127 

155 

0-3 

322 

120 

I 

120 

O.I 

1  2O 

1  20 

230 

0.15 

3OI 

1  80 

o-5 

"3 

0.05 

1  80 

"3 

328 

O.IO 

328 

290 

0.25 

"5 

0.025 

290 

"5 

595 

0.05 

375 

The  reaction  is  therefore  not  proceeding  in  proportion  to 
the  concentration  of  the  fibrinogen,  but  to  the  power  f  of  it. 
Closer  investigations  seem  desirable. 

Even  the  process  of  precipitation  is  subject  to  the  same 
influence  of  temperature  as  the  other  reactions  studied.2 
The  precipitating  substances  were  10  n.  sulphuric  acid  or 
albumen  precipitin,  produced  by  subcutaneous  injection 
of  egg-albumen  into  a  rabbit.  The  following  values  were 
observed  with  a  solution  of  2  c.c.  of  egg-albumen  in  98  c.c. 
of  physiological  salt-solution. 


10  N.  H2SO4  (90  MIN.) 


PRECIPITIN  (73  MIN.) 


TEMP. 

fobs. 

?calc. 

TEMP. 

?obs. 

?calc. 

35-8 

O.IO 

O.I  I 

36.1 

0.25 

0.25 

29.7 

0.16 

0.16 

3O.I 

0.30 

0.31 

25-4 

0.22 

0.21 

20.0 

0-45 

0.44 

19.9 

0.30 

0.29 

13-9 

o-55 

o-55 

14-5 

0.40 

0.41 

n  —  1 1,000.  n  =  6,300. 

1  Fuld:  Hofmeistcrs  Beitr'dge,  2.  514  (1902). 

2  Madsen  and  Walbum :   Oversigt  over  det  kgl.  danske  Vid-sdsks  Fork.  (1904), 


VELOCITY  OF   REACTION.      HOMOGENEOUS   SYSTEMS       93 

The  two  processes  are  undoubtedly  of  a  very  different 
nature.  Here  it  is  supposed  that  the  precipitins,  like  ren- 
net, obey  the  law  that  the  product  of  time  and  reacting  mass 
was  constant.  Then  if,  for  instance,  o.i  c.c.  of  10  n.  H2SO4 
acting  upon  8  c.c.  of  egg-albumen  solution  coagulates  it 
in  90  minutes  at  35.8°,  we  expect  that  0.3  c.c.  of  this  acid 
will  give  coagulation  in  30  minutes.  Now  this  quantity 
cogulates  the  egg-white  solution  in  90  minutes  at  19.9°. 
Therefore  we  say  that  the  velocity  of  reaction  is  three 
times  greater  at  35.8°  C.  than  at  19.9°  C.  In  this  manner 
the  variation  of  the  velocity  of  reaction  with  temperature 
may  be  calculated  and  from  that  the  value  of  p.  In  an 
analogous  manner  we  observe  with  the  precipitin  the 
quantity  necessary  to  give  a  unit  of  precipitate  in  a  given 
time,  and  from  this  we  calculate  the  different  times  in 
which  the  same  quantity  of  precipitin  will  give  the  same 
degree  of  precipitation  at  the  different  temperatures. 
Probably  a  closer  investigation  will  show  that  the  premises 
of  our  calculation  are  fulfilled. 

An  interesting  instance  of  a  bimolecular  reaction  has 
been  found  by  Madsen  and  Walbum1  in  the  interaction 
between  tetanolysin  and  pepton.  A  solution  of  2  g.  of 
Witte's  pepton  in  100  c.c.  water  and  another  of  2  per  cent 
tetanolysin  in  physiological  salt-solution  were  prepared. 
Mixtures  of  4  c.c.  of  the  solution  of  lysin  heated  to  36.i°C. 
with  o.  1 5, 0.20,  and  0.25  respectively  of  the  solution  of  pepton 
(of  36.1°)  and  so  much  physiological  salt-solution  of  36.1°, 
that  the  whole  equalled  8  c.c.  were  placed  in  a  water-bath 
at  this  temperature  and  the  haemolytic  power  determined 

1  Madsen  and  Walbum :    CentralbLf.  Bakteriologie,  40.  409  (1906). . 


94 


LECTURES  ON   IMMUNITY 


at  different  times.  For  this  purpose  a  part  of  the  mixture 
was  rapidly  cooied  in  a  test-tube  surrounded  by  ice,  whereby 
the  destruction  of  the  lysin  was  practically  brought  to  an 
end.  The  quantity  of  lysin  remaining  was  determined  in 
the  ordinary  manner  by  measuring  its  haemolytic  action 
upon  a  suspension  of  erythrocytes. 

In  this  manner  the  following  values  were  obtained :  — 


TIME 

0.15  c.c.  PEPTON  ADDED 

In  hours  #) 

i 

j 

Toxicity  (obs.) 

?calc. 

?obs. 

?calc. 

O 

IOO 

(55-8) 

0.0  1 

(0.0179) 

O.5 

47-7 

47-7 

0.021 

0.0210 

X 

39-7 

•    414 

O.O252 

0.241 

2 

30.3 

33-0 

0.0330 

0.0303 

4 

22.3 

23-4 

0.0448 

0.0427 

6 

18.1 

18.1 

0.0552 

0.0551 

8 

17 

14.8 

0.0588 

0.0675 

0.20  C.C. 

PEPTON  ADDED 

0 

IOO 

(60.0) 

0.0  1 

(O.OI67) 

o-S 

41.6 

41.6 

0.024 

0.024 

i 

30.3 

31.5 

0.033 

0.0313 

2 

20 

21.5 

0.050 

0.0460 

4 

12.2 

13-5 

0.082 

0.0754 

6 

9.6 

9-7 

0.105 

0.1048 

8 

8 

7-5 

0.125 

0.1342 

0.25  c.c. 

PEPTON  ADDED 

o 

IOO 

(70) 

0.0  1 

0.0142 

o-S 

35-2 

35-2 

0.0284 

0.0284 

i 

22 

234 

0.0455 

0.0426 

2 

13 

14.0 

0.0769 

O.O7II 

4 

6.0 

7.8 

o.i  666 

0.128 

6 

5-3 

54 

0.1886 

0.185 

8 

3'8 

4.1 

0.2631 

0.242 

VELOCITY  OF  REACTION.      HOMOGENEOUS  SYSTEMS       95 

Evidently  the  reaction  follows  very  nearly  the  law  for 
a  bimolecular  reaction,  in  regard  to  the  quantity  of  free 
toxin  (q),  so  that  :  — 


and: 


The  observed  and  calculated  values  agree  within  the 
errors  of  observation.  An  exception  is  evidently  displayed 
by  the  first  value  (t  =  o).  Just  as  in  similar  chemical 
processes  it  is  difficult  to  determine  the  time  zero,  since 
the  reaction  does  not  end  instantaneously  when  the  mix- 
ture is  removed  from  the  water-bath.  We  therefore  em- 
ploy the  same  method  that  has  been  applied  to  similar 
cases  studied  before,  namely,  to  reduce  the  time  to  that 
of  the  first  experimental  determination  of  the  toxicity, 
which  was  made  after  the  mixture  had  been  held  at 
36.1°  C.  for  half  an  hour. 

The  constant  (K)  increases  very  rapidly  with  the  con- 
centration of  the  pepton,  as  the  following  table  shows  :  — 

Concentration  of  pepton,  C         .  0.15  0.20  0.25 

Constant,  K,  obs.         .         .         .  0.0062  0.0147  0.0285 

Constant,  A",  calc.  =  1.833  C3      •  0.0062  0.0147  0.0286 

The  velocity  of  reaction  is  proportional  to  g*C3,  which 
may  be  explained  by  supposing  that  at  first  there  is 
formed  a  compound  of  two  molecules  of  tetanoysin 
with  three  molecules  of  peptone,  which  is  decom- 
posed very  rapidly  with  the  destruction  of  the  tetano- 
lysin. 


96 


LECTURES  ON  IMMUNITY 


Madsen  and  Walbum  have  also  investigated  the  influ- 
ence of  the  temperature  on  this  process,  which  in  this  case 
is  peculiarly  low,  p  being  found  to  be  10,500  only.  As 
a  comparison  we  may  cite  the  saponification  of  ethyl- 
acetate,  where  JJL  has  a  value  of  the  same  order  of  magni- 
tude, namely  11,160.  They  investigated  the  reaction 
velocity  of  a  solution  containing  4  c.c.  of  the  solution 
of  tetanolysin,  0.08  c.c.  of  a  2  per  cent  solution  of  Witte's 
pepton,  and  3.9  c.c.  of  physiological  salt-solution  at  37.1, 
31.2,  27.5,  and  17.8°  C.  respectively. 

They  found  the  following  figures :  — 

INFLUENCE  OF  THE  TEMPERATURE  ON  THE  DESTRUCTION  OF  TETANOLYSIN 

BY  PEPTON 


AT  37.1° 

AT  31.2° 

/  (hours) 

*obs. 

*calc. 

/  (hours) 

foW 

fete. 

O 

100 

100 

0 

100 

100 

0.33 

41.5 

41.7 

o-33 

46.7 

48.8 

I 

18.8 

18.9 

i 

26.3 

24.2 

2 

12.  1 

10.4 

2 

13.2 

13.8 

AT  27.5° 

AT  17.8° 

0 

100 

100 

0 

100 

100 

0-33 

48.9 

54-9 

0-33 

69.8 

69 

I 

28.3 

28.2 

I 

46.1 

40.8 

2 

I6.7 

16.4 

2 

21.5 

25-7 

4 

9-5 

8.9 

4 

13 

14.8 

The  agreement  between  the  observed  and  the  calculated 
values  is  very  satisfying;  even  at  17.8°  C.,  where  the  devi- 
ations are  the  greatest,  they  still  fall  within  the  possible 
errors  of  observation. 

The  calculated  constants  (K)  of  reaction,  according  to 
the  bimolecular  formula,  are  given  in  the  following  table 
O=  10,240):  — 


VELOCITY  OF  REACTION.     HOMOGENEOUS  SYSTEMS       97 


TEMP. 

•^obs. 

^calc. 

37-1 

0.0431 

0.0431 

31-2 

0.0313 

0.0313 

27-5 

0.0255 

0.0255 

17.8 

0.0144 

0.0144 

Here  the  coincidence  is  nearly  exact.  In  the  cases  in- 
vestigated above,  where  the  interval  of  temperature  reached 
only  four  degrees,  a  simple  exponential  formula  would  have 
given  just  as  good  results  as  the  more  complicated  one 
adopted  from  physical  chemistry ;  but  in  this  case  the 
interval  of  temperature  is  so  great  that  the  exponential 
formula  would  have  given  a  markedly  inferior  agreement 
with  the  observations,  though  still  the  differences  would 
not  have  exceeded  the  errors  of  observation. 

It  may  be  remarked  that  not  all  peptons  exert  this  weak- 
ening influence  on  tetanolysin ;  for  instance,  Chapeautaud's 
pepton  is  without  influence  in  this  respect. 

As  a  general  result  of  these  investigations  we  find  that 
the  spontaneous  destruction  of  the  substances  studied  in- 
creases in  solution  very  rapidly  with  temperature.  In 
most  cases  the  destruction  of  these  substances  by  cata- 
lytic agencies  increases  much  more  slowly,  about  at  the 
same  rate  as  the  catalytic  processes  studied  in  general 
chemistry. 

The  observed  values  of  //.  are  compared  in  the  following 
table :  — 

Spontaneous  destruction  of  dry  emulsin  /*  =  26,300 

(Tammann) 

Spontaneous  destruction  of  lipase  from  castor  beans  in  sol.  //,  —  26,000 

(Nicloux,  cf.  next  chapter) 

Spontaneous  destruction  of  emulsin  in  0.5  per  cent  sol.  /*  =  45,000 

(Tammann) 


98 


LECTURES  ON  IMMUNITY 


Spontaneous  destruction 
Spontaneous  destruction 
Spontaneous  destruction 
Spontaneous  destruction 
Spontaneous  destruction 
Spontaneous  destruction 
Spontaneous  destruction 


of  trypsin  in  2  per  cent  sol. 

of  pepsin  in  2  per  cent  sol. 

of  rennet  in  2  per  cent  sol. 

of  vibriolysin  in  sol. 

of  tetanolysin  in  sol. 

of  comp.  haemolysin  in  sol. 

of  dibromsuccinic  acid 


M=  62,034 

/* 
At 

M 
H 
M 
A* 


Destruction  of  salicin  by  emulsin 
Destruction  of  cane  sugar  by  invertase 

Destruction  of  tetanolysin  by  pepton 
Destruction  of  coli-agglutinin  by  trypsin 
Coagulation  of  milk  by  rennet 
Coagulation  of  digestion  of  casein-salt  by  trypsin 
Precipitation  of  egg-white  by  sulphuric  acid 
Precipitation  of  egg-white  by  pr^cipitin 
Digestion  of  gelatin  by  means  of  pepsin 
Digestion  of  gelatin  by  means  of  trypsin 
Digestion  of  egg-white  by  means  of  pepsin 
Hydrolysis  of  sugar  by  acids 


/*  = 


Saponification  of  cotton  oil  by  lipase  from  castor  beans       /x 

(Nicloux, 

Saponification  of  triacetin  by  lipase  from  castor  beans         /A 

(A.  E.  Taylor, 
Saponification  of  ethyl-acetate  by  NaOH  ju, 


=  90,000 
=  128,000 
=  162,000 
=  198,500 
=  22,220 

(van't  Hoff 
=      3,300 

(  ?  Tammann) 
9,080 

(Kjeldahl) 
10,240 
16,500 
20,650 
29,500 
11,000 
6,300 
10,750 
10,570 
15,570 
25,600 

(Spohr) 
=      7,540 
cf.  next  chapter) 
=    16,700 
cf.  next  chapter) 

=    11,15° 

(Warder) 


/*  = 


The  spontaneous  destruction  of  the  different  substances 
investigated  by  Madsen  increases  from  three  to  nine  times 
more  rapidly  with  temperature  than  the  corresponding 
phenomenon  .  for  dibromsuccinic  acid  (C4H4O4Br2  = 
C4H3O4Br  +  HBr).  The  values  of  p  found  by  Madsen 
even  exceed  those  found  for  emulsin  by  Tammann.  On 
the  other  hand,  the  M  for  the  catalytic  actions  is  of  the 
same  order  of  magnitude  as  those  known  heretofore  (espe- 
cially that  of  Saponification).  The  similarity  of  the  values 


VELOCITY  OF  REACTION.     HOMOGENEOUS  SYSTEMS       99 

of  p  in  the  two  cases  of  digestion  of  gelatin  by  means  of 
pepsin  or  of  trypsin  is  very  startling.  In  any  case  it  is  not 
possible  to  retain  the  opinion  that  /-i  is  of  the  same  order 
of  magnitude  for  all  velocities  of  reaction,  corresponding 
closely  to  an  increase  in  the  proportion  i  :  2  for  an  increase 
in  temperature  of  ten  degrees  (fi  =  1 1,850  at  20°,  p  =  14,400 
at  50°,  and  /*=  17,200  at  80°  C.).  As  most  of  Madsen's 
determinations  were  carried  out  in  the  proximity  of  50°,  we 
may  say  that  /*  is  between  four  and  fourteen  times  greater, 
that  is,  the  increase  for  10°  C.  may  be  from  28  =  8  to  213  = 
8200  times  the  usual  rate. 


COLLEGE   OF   DENTISTRY 

UNIVERSITY  OF  CALIFORNIA 


CHAPTER   IV 
VELOCITY   OF  REACTION.     HETEROGENEOUS   SYSTEMS 

MOST  of  the  reactions  concerned  in  sero-therapy  occur 
in  heterogeneous  systems,  and  may  therefore  be  regarded 
as  analogous  to,  e.g.,  the  solution  of  a  metal  or  a  carbonate 
in  an  acid.  To  this  category  belong,  for  instance,  the 
haemolytic  reactions,  which  possess  such  great  importance 
for  theoretical  researches.  Madsen  and  I l  have  made 
some  experiments  on  the  velocity  of  haemolysis  by  sodium 
hydrate,  ammonia,  and  tetanolysin.  The  reagents,  solu- 
tions of  the  haemolytic  substances  and  suspensions  of 
blood-emulsions,  were  heated  to  37°  C.,  mixed  and  allowed 
to  act  upon  each  other  for  a  certain  time,  then  the  mixture 
cooled  down  to  o°  C.  in  order  to  practically  check  the  re- 
action, and  rapidly  centrifugalised.  The  colour  of  the 
solution  indicates  the  degree  of  haemolysis. 

The  velocity  of  the  reaction  was  calculated  under  the 
assumption  that  the  transformed  quantity  in  the  unit  time 
is  proportional  to  the  number  of  erythrocytes  present. 
The  haemolytic  agent  was  present  in  such  an  excess  that 
its  quantity  was  many  times  greater  than  that  necessary 
for  complete  haemolysis.  This  quantity,  being  in  excess, 
was  therefore  regarded  as  approximately  constant  during 
the  short  time  of  reaction.  Hence  the  velocity  of  reaction 
should  be  that  of  monomolecular  order  in  a  homogeneous 

1  Festskrift,  Copenhagen  (1902),  No.  3. 
100 


VELOCITY  OF  REACTION.     HETEROGENEOUS  SYSTEMS     lot 

system.      A  series  of  experiments  with  0.5  c.c.  o.i  n.  NH3 
mixed  with  10  c.c.  2.5  per  cent  suspensions  of  blood  gave: 

Time  (minutes)  o  6  14  23  31 

Intact  blood  (per  cent)    100  97  82  60  35 

Constant  of  reaction         —  0.00022          0.0062  0.0096          0.0147 

The  "constant"  increases  very  rapidly  as  the  process 
advances.  This  phenomenon  depends  evidently  upon 
something  similar  to  the  "time  of  induction,"  observed  in 
reactions  in  heterogeneous  and  sometimes  also  in  homoge- 
neous systems  (action  of  light  upon  a  mixture  of  chlorine 
and  hydrogen).  In  this  case  it  is  easy  to  understand  that 
a  certain  quantity  of  ammonia  must  diffuse  into  the  erythro- 
cytes  and  act  there  for  some  time  before  the  haemoglobin 
leaves  the  cells.  According  to  different  circumstances, 
such  as  varying  resisting  power  of  the  cells,  distance  from 
the  molecules  of  ammonia  in  the  moment  of  mixing,  the 
different  cells  are  attacked  more  or  less  slowly. 

Still  it  was  possible  to  prove  that  the  time  necessary  for 
haemolysing  a  given  number  of  erythrocytes  is  inversely 
proportional  to  the  strength  of  the  haemolytic  agent.  Thus, 
for  instance,  in  experiments  with  solutions  the  dilutions 
(inverse  concentrations)  of  which  were  proportional  to 
1:0.44:0.23:0.133  the  following  times  in  minutes  were 
necessary  for  the  haemolysis  of  3,  10,  20,  30  and  40  per 
cent  respectively  of  the  erythrocytes.  In  parentheses  are 
printed  the  calculated  values  obtained  according  to  the 
rule  mentioned. 

Haemolysis  310  20  30  40  per  cent. 

Dilution  i         13  (13)  26    (26)      35  (35)      44  (44)      53  (53)      min. 

Dilution  0.44    6  (5.7)  10    (11.5)   15  (15.4)   18  (19.4)  23  (23.3)  min. 

Dilution  0.23      5.5(6.0)     9(8.0)     12  (10.1)  14  (12.2)  min. 

Dilution  0.133    i-8  (3.5)     4(4-7)        6.2(5.9)    8(7.1)    min. 


IO2  LECTURES  ON  IMMUNITY 

The  agreement  is  very  satisfactory. 

Similar  experiments  were  done  with  sodium  hydrate  and 
tetanolysin.  They  led  to  similar  results.  If  different 
quantities  of  ammonia  are  allowed  to  act  upon  a  unit 
amount  of  blood  corpuscles  during  a  given  time,  it  fol- 
lows from  the  considerations  given  above  that  the  haemo- 
lysed  quantity  increases  more  rapidly  than  in  proportion 
to  the  amount  of  ammonia.  If  we  consider  the 
quantities  a  and  2  a,  and  let  the  first  act  during  the 

time  -,  the  second  during  the  time  /,  the  action  of  the  two 
will  be  equal.  If  thereafter  the  quantity  a  be  allowed  to 
act  during  the  time  -,  the  velocity  of  reaction  will  be  much 

greater  during  this  interval  than  in  the  first  period.  There- 
fore the  quantity  haemolysed  in  the  time  /  by  the  quantity 
2  a  is  more  than  double  that  haemolysed  in  the  same  time 
by  the  quantity  a  (provided  that  the  total  haemolysis  is  not 
near  completeness,  and  that  we  observe  in  the  first  stages 
of  the  process).  It  is  often  found  that  the  quantity  haemo- 
lysed is  roughly  proportional  to  the  square  of  the  concen- 
tration of  the  poison,  if  this  does  not  act  very  rapidly  as  is 
the  case  with  ammonia  and  tetanolysis.  This  rule,  which 
may  be  of  use  for  many  calculations,  is  illustrated  by  the 
following  examples  (a  is  the  concentration  of  the  poison, 
b  the  degree  of  haemolysis  in  per  cent,  c  =  V#  :  a). 

In  other  cases,  generally  of  rapidly  acting  haemolytic 
agents,  the  rule  does  not  hold,  but  the  value  of  c  sinks 
rapidly  when  the  degree  of  haemolysis  falls  below  10  per 
cent.  Such  are  the  strongly  dissociated  bases,  caustic 
potash,  soda,  and  lithium,  and  even  solanin. 


VELOCITY  OF  REACTION.      HETEROGENEOUS   SYSTEMS     103 


INFLUENCE  OF  THE  CONCENTRATION  OF  A  POISON  ON  THE  HAEMOLYSIS 


TETANOLYSIN 

AMMONIA 

a 

b 

si 

c=  — 
a 

a 

b 

c-  — 
a 

O.QI 

45 

7-4 

0.84 

65 

9.6 

0.74 

25 

6.8 

0.67 

55 

n.  i 

°-57 

H 

6.6 

0.50 

37 

12.3 

0.48 

7 

5-5 

0.40 

27 

12.0 

043 

6 

5-7 

0.36 

16 

II.  I 

o-38 

3-5 

5-9 

0.31 

12 

II.  I 

0.29 

2-5 

5-5 

0.27 

6 

9.2 

0.24 

2-5 

6.6 

0.22 

5 

10.2 

0.20 

1-7 

6.5 

The  blood  often  binds  a  certain  quantity  of  the  poison 
added,  so  that  under  a  certain  concentration  no  haemolysis 
occurs ;  this  was,  e.g.,  the  case  with  10  c.c.  of  a  suspension 
containing  10  per  cent  of  erythrocytes  and  less  than 
0.015  milligramme  equivalent  of  caustic  soda  or  ammonia. 
The  quantity  bound  is  very  strictly  proportional  to  the 
quantity  of  erythrocytes. 

An  analogous  case  is  seen  in  telanolysin,  according  to 
the  experiments  of  Madsen  and  Henderson-Smith.  They 
added  different  quantities,  q,  of  telanolysin  to  10  c.c.  of 
2  per  cent  suspension  of  erythrocytes  from  the  horse  and 
determined  the  times  which  were  necessary  at  37°  C.  to 
produce  a  certain  degree  of  haemolysis.  The  results  are 
given  below  on  p.  104. 

The  time  oo  indicates  that  the  quantity  0.25  telanolysis 
does  not  give  an  appreciable  haemolysis.  Evidently  the 
product  of  the  reacting  quantity  (^  — 0.25)  and  the  time  of 
action  is  constant. 


IO4 


LECTURES  ON  IMMUNITY 


H^MOLYSIS  BY  MEANS  OF  DIFFERENT  QUANTITIES  OF  TETANOLYSIN 
AT  37°  C. 


q 

t  (min.) 

(7-0.25)  t 

q 

t  (min.) 

(q—  0.25)  t 

1.0 

2 

1.50 

0.4 

11.8 

1.77 

0.8 

2.8 

1-54 

o-35 

13-5 

i-35 

0.6 

4-5 

1.48 

0-3 

28.5 

1.42 

o-5 

6.1 

1.52 

0.25 

oo 

0-45 

7-i 

1.42 

The  agglutinins  display  in  their  general  behaviour  a 
very  great  similarity  to  the  hsemolysins.  This  was  de- 
termined by  experiments  in  which  different  quantities,  q, 
of  an  agglutinin  (against  Bacillus  coli)  were  allowed  to 
act  upon  similar  suspensions  of  this  bacillus  at  37°  C. 
Then  the  time  necessary  to  produce  a  given  degree  of 
agglutination  was  found  to  be  inversely  proportional  to  q 
as  will  be  seen  from  the  following  table. 

Action  of  different  quantities  of  agglutinin  on  Bacillus  coli 
atlfC. 


q 

t  (min.) 

qt 

q 

t  (min.) 

qt 

0.08 

2O 

(1.6) 

0.008 

140 

(1,12) 

0.035 

30 

1.05 

0.006 

150 

0.90 

0.025 

45 

I.  II 

0.0055 

I65 

0.91 

0.017 

60 

1.02 

0.005 

1  80 

0.90 

0.012 

90 

1.08 

0.004 

210 

0.84 

O.OOS 

120 

0.96 

0.0035 

240 

0.84 

O.OO5 

1  80 

0.90 

0.003 

300 

0.90 

O.OO4 

240 

0.96 

O.OO22 

420 

0.92 

0.003 

300 

0.90 

0.002 

480 

0.96 

O.O027 

360 

0.97 

Mean   0.99 

Mean    0.90 

VELOCITY  OF  REACTION.  HETEROGENEOUS  SYSTEMS  1 05 

The  first  figures  indicate  an  activity  known  to  be  too 
low  (too  long  time).  This  may  be  due  to  errors  in  the 
measuring  of  the  time.  It  is  supposed  that  the  liquids  are 
immediately  brought  to  the  temperature  of  the  thermostat 
in  which  they  are  placed.  Evidently  this  is  not  quite  true, 
and  therefore  in  a  more  exact  calculation  a  certain  time 
should  be  subtracted  from  the  observed  one. 

Henri  has  carried  out  some  interesting  experiments  on 
the  haemolysis  of  chicken  erythrocytes  by  means  of  normal 
dog-serum.  He  added  different  quantities  of  the  serum 
to  30  c.c.  of  a  10  per  cent  suspension  of  the  erythrocytes 
and  so  much  of  0.9  per  cent  NaCl  solution  as  to  bring 
the  whole  volume  to  40  c.c.  Then  he  observed  that  the 
haemolysis  proceeded  at  first  rapidly,  later  on  more  slowly, 
until  it  reached  a  limit  value.  This  value  was  found  to 
be:  — 

Quantity  of  serum  in  c.c.  (<j)        0.3        0.4        0.5       0.75         I         1.5 
Limit  of  haemolysis  in  per  cent   15          19.5          30          56       93        100 

93  &  lS-3      23.5         33         60      93      (100) 

The  limit  value  increases  more  rapidly  than  the  first 
power  of  the  quantity  of  serum,  but  not  as  much  as  the 
square  of  it;  the  last  figures  indicate  that  the  limit  is 
nearly  proportional  to  the  power  f  of  q. 

To  illustrate  the  progress  of  haemolysis  with  time  Henri 
gives  the  following  figures :  — 

Quantity   of   serum 

in  c.c 0.15    0.2      0.3       0.4         0.5     0.75  I  1.5         2 

Haemolysis    in    per 
cent  after  12  min.   —        —      —        —  —          —          8.5          19.1        30 

(8.5)      (19.1)     (34) 
Haemolysis    in    per 

cent  after  36  min.    —        —      5.0      6.9        10.0      28.2       66.6         95.6       — 
(4.5)    (8.0)     (12.5)   (28.1)     (50)       (100) 


io6 


LECTURES  ON  IMMUNITY 


Haemolysis    in   per 

cent  after  76  min.  —  4.1  8.4  13.0  19.5  47.0  78.5  98.3  100 

(3-i)  (7-0)  (12.5)  (19.5)  (43.9)  (78)  (100)  (100) 
Haemolysis    in    per 

cent  after  107  min.  3.3  5.5  11.7  15.7  23.6  50.0  85.0  100  100 

(2.0)  (3.6)  (8.0)  (14.3)  (22.3)  (50.0)  (89.0)  (100)  (loo) 
Haemolysis    in    per 

cent  after  200  min.  4.8  7.9  14.4  18.3  29.0  55.0  90.0  100  100 

(2.4)  (4.3)  (9.6)  (17.1)  (26.7)  (60)  (ico)  (100)  (100) 

In  the  brackets  are  written  the  figures  which  are  pro- 
portional to  the  squares  of  the  quantities  of  haemolysing 
serum.  As  will  be  seen  from  these,  the  agreement  with 
the  observed  figures  is  fairly  good  (within  the  errors  of 
observation),  if  the  time  lies  below  76  minutes  (in  most 
cases  the  time  of  reaction  was  about  one  hour  in  similar 
experiments).  For  longer  times  of  reaction  the  action  of 
small  quantities  is  somewhat  greater  than  the  rule  of  the 
square  root  demands. 

Henri1  found  that  the  progress  with  time  follows  very 
closely  the  law  of  monomolecular  reactions.  He  mixed 
30  c.c.  of  a  10  per  cent  suspension  of  chicken  erythro- 
cytes  with  9.5  c.c.  of  0.8  per  cent  sodium  chloride  solu- 
tion and  the  following  quantities  of  dog-serum.  The 
haemolysis,  x>  is  given  with  its  limit  value  as  unit.  The 
reaction-constants  are  calculated  from  the  formula 

^     l^          l 

K  =-log . 

/     &  i  —  x 


Quantity  of  serum  in  c.c. 

o-3 

0.4 

0-5 

0-75 

x        K 

x        K 

x        K 

x        K 

Time  of  reaction,  24  min. 

0.33    0.0072 

0.35    0.0077 

0.33    0.0072 

0.50    0.0125 

Time  of  reaction,  63  min. 

0.56   0.0057 

0.67    0.0076 

0.65    0.0072 

0.83      0.0122 

Time  of  reaction,  94  min. 

0.78    0.0070 

0.80    0.0094 

0.79    0.0072 

0.90    0.0106 

Time  of  reaction,  190  min. 

0.96   0.0071 

0.94    0.0065 

0.96    0.0071 

0.98      0.0090 

1  Victor  Henri:   C.  r.  de  la  Societe  Biologique,  58.  36-39  (Jan.  4,  1605). 


VELOCITY  OF  REACTION.     HETEROGENEOUS  SYSTEMS     IO/ 

Another  series  of  experiments  seems  to  indicate  that 
the  value  of  K  is  independent  of  the  quantity  of  erythro- 
cytes,  but  increases  more  rapidly  than  in  proportion  to  the 
quantity  of  serum.  (It  is  rather  peculiar  that  this  behaviour 
is  not  indicated  in  the  figures  given  above.) 

Madsen,  aided  by  Walbum  and  Nugochi,  has  carried  out 
a  large  number  of  experiments  on  the  velocity  of  reactions 
of  different  substances  at  different  temperatures.  Their 
method  consisted  in  determining  the  qualities  of  the  same 
agent,  e.g.  haemolysin,  which  were  necessary  to  produce  a 
certain  effect  in  a  given  time,  e.g.  10  minutes.  The  lower 
the  temperature,  the  greater  the  quantity  of  the  agent 
necessary  for  the  effect,  generally  speaking.  Taking 
ammonia  as  an  illustration,  we  know  that,  if  the  quan- 
tity exceeds  greatly  the  amount  necessary  for  complete 
haemolysis  in  a  very  long  time,  the  time  necessary  to 
secure  a  certain  effect  is  inversely  proportional  to  the 
quantity  of  ammonia  used.  If  therefore,  as  the  experi- 
ments indicate,  the  addition  of  0.085  c-c-  of  a  solution  of 
ammonia  to  8  c.c.  of  a  i  per  cent  suspension  of  erythro- 
crytes  from  horse  blood  at  34.8°  C.  will  give  in  10  minutes 
the  same  effect  as  0.17  c.c.  of  the  same  solution  at  29.7°  C., 
the  other  conditions  being  the  same,  we  conclude  that  0.085 
c.c.  of  the  ammonia  would  require  20  minutes  at  29.7°  C.  to 
attain  the  same  effect  as  in  10  minutes  at  34.8°;  i.e.  the 
velocity  of  reaction  at  34.8°  C.  is  double  that  at  29.7°  C. 
Generally  speaking,  the  velocity  of  reaction  is  in  these 
experiments  inversely  proportional  to  the  quantity  used. 
Evidently  this  conclusion  is  valid  only  for  those  cases  in 
which,  as  for  ammonia,  the  rate  of  the  reaction  is  propor- 
tional to  the  quantity  of  reacting  substance;  but  this  seems 


io8 


LECTURES  ON  IMMUNITY 


to  be  generally  the  case  if  a  correction  be  introduced  for 
the  first  fraction  of  the  poison,  which  is  neutralized  in 
the  erythrocytes.  This  correction,  in  most  cases,  seems 
to  be  of  minor  importance. 

We  may  again  use  the  formula  — 


where  v1  and  z/0  indicate  the  velocities  at  the  absolute  tem- 
peratures 7^  and  T0  and  p  is  a  characteristic  constant.  Here 
we  have  only  to  replace  the  velocity,  v,  by  the  inverse  value 
of  the  concentration  necessary  to  produce  the  desired  effect. 
Experimentally  it  was  found  that  the  results  agreed  very 
well  with  the  formula,  as  'shown  by  the  following  figures, 

AMMONIA,  0.5  NORMAL  SOLUTION 


*=  10  Mm. 

2=20  MlN. 

z  —  30  MIN. 

t              fobs.          ?calc. 
39.5        0.04         0.043 

34.8      0.085     °-°83 

29.7        0.17         0.17 
25.9        0.3            0.3 
21.0        0.60         0.64 

\i.—  26,760 

t             ?obs.         ?calc. 
39.2        0.03         0.029 
34.8        0.05          0.05 
30.2        0.085       °'°81 
25.7        0.19         0.17 
21.  0        0.3            0.32 
15.7        0.55         0.69 
/A  =24,  360 

/              fobs.         tf'calc. 
39-5        0.027       0.023 

34.8      0.035     °-°39 

29.7        0.07         0.072 

25-9      0-13       0.12 

21.0        0.25          0.23 

15.2    0.5      0.5 

/*  =  23,020 

*=6o  Mm. 

s=iooMm. 

jz=i8o  MIN. 

t              fobs.         ?calc. 
39.2        0.019       0.014 
34.8        0.024       0.022 

30.2      0.035     °-°35 

25.7        0.050       0.056 
15.7        0.17         0.17 
12.2        0.26          0.26 

At  =19,150 

/             fobs.         ^calc. 
39.1         0.02          O.OlS 
34.6        0.025       0.025 
30.7        0.025       0.034 

25.9      0.045     O-OS1 
21.3      0.060     0.075 
16.1       0.115     0.12 

12.2         0.17          0.17 
/i  =  14,920 

t              ?obs.         ?calc. 
39.O        O.OI5       O.OI5 

34.7      0.185     °-l85 

30.9        O.O23       O.O23 
25.7        0.030       0.029 
21.5        0.040       0.037 

1  6.  i       0.050     0.050 
/*  =  9»44i 

VELOCITY  OF  REACTION.     HETEROGENEOUS   SYSTEMS     1 09 

giving  the  observed  concentrations  compared  with  cal- 
culated values;  z  gives  the  time  of  reaction,  t  the  temper- 
ature, q  the  quantity  added,  i.e.  the  inverse  value  of  the 
velocity  v. 

As  will  be  seen  from  these  figures  the  formula  may  be 
well  used  in  this  case.  We  observe  also  that  the  magnitude 
/i  increases  with  decreasing  time  of  reaction.  With  a  pro- 
longed reaction-time,  the  quantities  of  ammonia  used  do 
not  exceed  very  much  the  quantity  necessary  for 
total  haemolysis  and  then  our  premises  are  not  fulfilled. 
Hence  the  real  value  of  /<&,  corresponding  to  the  theo- 
retical premises,  is  that  to  which  the  values  of  ^  converge 
with  decreasing  time  of  reaction.  It  does  not  seem  to 
differ  very  much  from  that  valid  for  z  =  10  min.  The  appli- 
cability of  the  known  equation  from  physical  chemistry  for 
even  longer  times  renders  it  highly  probable  that  it  would 
hold  for  the  limit-value,  which  would  be  reached  in  an  ex- 
ceedingly short  time  of  observation,  if  it  were  possible  to 
observe  it  directly.  In  heterogeneous  systems  the  direct 
observation  of  the  velocity  of  reaction  meets  in  most  cases 
with  great  difficulties,  as  has  been  indicated  above,  so 
that  the  indirect  observations  such  as  those  executed  by 
Madsen,  Noguchi,  and  Walbum  are  necessary  to  obtain 
a  knowledge  of  these  phenomena.  I  therefore  reproduce 
the  values  of  p  found  by  them  for  different  bases  and 
acids.  The  interval  of  temperature  was  always  between 
about  17  and  39°  C.  The  experiments  were  arranged  in 
the  same  manner  as  those  dealing  with  ammonia. 

These  figures  give  occasion  to  remarks  similar  to  those 
made  regarding  the  behaviour  of  ammonia.  If  we  could 
carry  out  experiments  extended  through  a  very  long  time, 


110 


LECTURES  ON   IMMUNITY 


0.2  n.  SODIUM 

o  2  n.  POTAS- 

o.i n.  FORMIC 

i  n.  ACETIC 

i  n.  PROPIENIC 

i  n.  BUTYRIC 

HYDRATE 

SIUM  HYDRATE 

ACID 

ACID 

ACID 

ACID 

Time 

Time 

Time 

Time 

Time 

Time 

min.         ^ 

min- 

c- 

min. 

min. 

nun. 

f- 

min.     ^ 

10   15,200 

10   11,700 

10      8,800 

10  23,600 

10  24,900 

10    21,600 

20       9,500 

20 

9,200 

2O      7,600 

15    22,2OO 

20    1  8,  100 

20    19,900 

30       9,400 

30 

8,300 

30      4,300 

20  18,  100 

30    15,900 

30    15,200 

40     9,200 

40 

8,000 

40      2,600 

40   15,500 

40 

15,100 

40    14,000 

50       7,400 

60 

6,100 

50      2,900 

50  14,200 

60 

13,700 

50    13,200 

60     7,200 

120 

5,200 

180        900 

60   13,200 

90 

7,700 

80     6,900 

180     4,100 

90     8,800 

120 

5,100 

loo     6,300 

1  20     7,500 

180 

4,800 

180     5,700 

2IO       5,IOO 

i  n.  MALEINIC  ACID 

i  n.  CITRACONIC  ACID 

i  n.  ITACONIC  ACID 

o.i  n.  OLEINIC  ACID 

Time                „ 

Time              „ 

Time              „ 

Time             „ 

min. 

min. 

min. 

min. 

10         12,700 

10          13*500. 

15             17,000 

10         25,800 

20           9,100 

20             11,700 

20             I5,60O 

22            23,400 

30               8,300 

50                4,400 

the  temperature  would  probably  exert  a  very  minute  influ- 
ence. To  attain  a  certain  effect,  for  instance  total 
haemolysis  or  the  first  appreciable  trace  of  haemolysis,  a 
certain  amount  of  acid  or  base  would  be  necessary,  equiv- 
alent to  the  quantity  of  erythrocytes  present.  Madsen  and 
I  found  the  following  values  (q)  of  0.05  n.  NaOH  or 
0.037  n-  NH3  to  be  the  greatest  quantities  which  could 


NaOH 

NH3 

n 

?obs. 

?calc. 

^obs. 

?calc. 

20 

0.60 

0.60 

0.82 

0.82 

10 

0.27 

O.3O 

0.42 

0.41 

5 

0.14 

O.I5 

O.I9 

0.20 

2.5 

0.09 

0.075 

O.I  I 

O.IO 

1.25 

0.047 

0.038 

0.055 

O.O5 

0.62 

0.018 

O.OI9 

0.027 

0.025 

0.31 

O.OII 

O.OIO 

0.014 

0.013 

VELOCITY  OF  REACTION.     HETEROGENEOUS  SYSTEMS     III 

be  added  without  producing  a  sensible  effect  on  10  c.c. 
of  an  n  per  cent  suspension  of  horse-blood. 

The  calculated  values  are  obtained  under  the  assumption 
that  0.6  c.c.  of  the  0.05  n.  NaOH  solution,  which  corresponds 
to  0.082  c.c.  of  the  0.037  n.  NH3  solution,  are  equivalent  to 
10  c.c.  of  a  20  per  cent  suspension  in  producing  the  first 
trace  of  haemolysis.  This  idea  of  the  equivalency  is  evi- 
dently true,  though  the  time  of  reaction  was  here  only  one 
hour  at  37°  C.  To  this  corresponds  indeed  the  fact  found 
by  Madsen  and  Walbum  that  equivalent  quantities  of  the 
four  bases  investigated  (namely,  NH3,  NaOH,  KOH,  and 
Ba(OH)2)  must  be  added  to  the  same  quantity  of  blood  to 
produce  the  first  trace  of  haemolysis.  For  19  different  acids 
the  corresponding  quantity  was  in  all  cases  equivalent,  but 
it  was  double  as  great  as  for  the  bases.  The  time  of 
reaction  was  24  hours  at  16.2°  C.  Here  we  have  evidently 
not  to  do  with  a  velocity  of  reaction,  but  with  a  strong 
chemical  binding  of  the  acids  or  the  bases  to  some  sub- 
stance in  the  erythrocytes. 

The  same  is  true  according  to  the  experiments  of 
Madsen,  Walbum,  and  Noguchi 1  even  for  the  other  reaction 
which  they  observed,  which  was  not  far  from  complete 
haemolysis,  if  we  regard  the  figures  for  prolonged  times  and 
high  temperature  (37-39°),  where  the  reaction  has  nearly 
come  to  an  end.  The  three  bases  yield  for  this  end-value : 
KOH,  0.008;  NaOH,  0.008;  and  NH3,  0.0075  c.c.  respec- 
tively of  i  n.  solutions;  within  the  errors  of  observation 
these  quantities  are  equivalent.  For  the  acids  examined 
we  find  the  following  figures  (in  c.c.  of  i  n.  solutions): 
formic,  0.012;  acetic,  0.015 ;  propionic,  0.017;  butyric,  0.017; 

1  Madsen,  Noguchi,  and  Walbum :   Oversigtt  1904,  No.  6,  pp.  425  and  447. 


112  LECTURES  ON  IMMUNITY 

maleinic,  0.013;  an(i  citric  acid,  0.012.  These  figures  do  not 
differ  very  much  from  each  other;  they  are  really  a  little 
higher  for  the  weaker  than  for  the  stronger  acids,  perhaps 
indicating  a  slightly  marked  hydrolytic  effect.  But  on  the 
whole  they  indicate  a  combination,  although  of  not  quite  so 
strong  a  nature  as  with  the  bases.  For  very  long  times  of 
reaction  we  therefore  observe  no  real  velocity  of  reaction, 
but  a  binding,  and  hence  we  might  expect  that  for  these 
long  times  of  reaction  the  values  of  /*  converge  to  zero. 
This  convergence  takes  place  much  earlier  for  the  strong 
acids  and  bases,  which  react  more  rapidly,  than  for  the 
weak  ones.  Thus,  for  instance,  a  dosage  of  o.i  c.c.  normal 
NH3  needs  210  minutes  to  yield  the  same  haemolytic  effect 
that  the  equivalent  quantity  of  the  three  strong  bases  exam- 
ined give  in  15  minutes  (at  16.2°);  and  an  addition  of  0.05 
c.c.  of  dichloracetic  acid  produces  the  same  hasmolytic 
effect  in  5  minutes  as  the  equivalent  quantity  of  acetic  acid 
in  60  minutes.  Therefore  even  the  shortest  time  (10 
minutes)  used  in  these  investigations  of  strong  acids  or 
bases  seems  to  be  much  too  long  to  give  a  value,  ft0,  for  ft, 
which  approaches  that  for  an  infinitely  short  time,  corre- 
sponding to  the  real  value  for  the  velocity  of  reaction.  On 
the  other  hand,  the  values  for  the  shortest  times  for  weak 
acids  do  not  differ  much  from  each  other,  and  probably 
also  not  from  the  theoretical  limit-value,  which  seems  to 
be  about  p=  27,000.  A  little  higher,  perhaps,  lies  the  true 
limit-value  for  ammonia,  p=  29,000.  These  limit-values  are 
probably  valid  even  for  the  other  acids  and  bases.  The 
great  difference  in  the  speed  of  reaction  between  the  strong 
and  the  weak  bases  and  acids  seems  to  indicate  that  we 
have  even  here  to  do  with  an  ionic  reaction,  although  the 


VELOCITY  OF  REACTION.     HETEROGENEOUS  SYSTEMS     113 


differences  would  be  much  greater  than  those  observed 
if  the  phenomenon  were  not  disturbed  by  the  relatively 
long  time  of  observation. 

Oleic  acid  differs  rather  widely  from  the  other  acids, 
exhibiting  the  same  effect  as  about  five  times  larger  quan- 
tities of  other  weak  acids.  The  haemolytic  agent  in  this 
acid  is  therefore  probably  not  only  the  hydrogen  ion,  as  in 
other  acids,  but  the  undissociated  molecules  exert  also 
a  haemolytic  action. 

The  lysins  of  bacterial  origin  reach  the  end-value  of 
their  haemolytic  effect  much  more  slowly  even  than 
ammonia.  Hence  it  is  probable  that  the  deduced  value  of 
p  for  these  substances  does  not  differ  materially  from  the 
theoretical  value.  I  reproduce  some  figures  from  Madsen 
and  Walbum's  series  :  — 

INFLUENCE  OF  TEMPERATURE  ON  THE  ACTION  OF  LYSINS  OF  BACTERIAL 

ORIGIN 


STREPTOLYSIN  (20  MIN.) 

VlBRIOLYSIN  (20  MlN.) 

TETANOLYSIN  (60  MIN.) 

Temp. 

fobs. 

?calc. 

Temp. 

fob*. 

ftffc. 

Temp. 

fobs. 

*cale. 

36.1 
3I-I 
25.8 
22.9 

0.08 
0.20 
0.40 
1.30 

0.08 
0.21 
0-54 
I.I5 

35-3 
29.8 
26.3 
20.  6 

0.17 
0.25 
0.4 
I.O 

0.10 

0.25 
0.4 

I.O 

30.4 
25.6 
21.9 
154 

0.40 
0.50 
0.80 

1.  00 

o-37 
0-53 
0.66 

I.OO 

I2.I 

1.30 

1.27 

ju=  31,900 

H  =  27,300 

A*  =  10,900 

The  values  of  /*  for  streptolysin  and  vibriolysin  probably 
do  not  differ  very  much  from  the  limit-value,  /*0.  A  com- 
parison of  the  observed  with  the  calculated  values  seem 
to  indicate  rather  great  errors  of  observation,  which  make 
the  value  of  //.  relatively  uncertain.  For  vibriolysin,  there 


LECTURES  ON  IMMUNITY 


are  given  four  values  corresponding  to  the  times,  20,  40, 
100,  and  180  minutes  respectively ;  they  are  27,300,  24,400, 
19,300,  and  15,800  respectively.  They  seem  to  indicate 
that  the  limit-value  lies  a  little  above  27,300,  but  the  calcu- 
lation would  give  a  better  agreement  if,  in  the  first  in- 
stance, /*>  were  fixed  at  25,000,  which  value  therefore  per- 
haps comes  near  to  the  end-value.  The  only  statement 
that  can  be  made  is  that  these  values  are  of  nearly  the  same 
magnitude  as  those  for  the  haemolytic  action  of  (weak) 
acids  and  bases,  and  that  a  closer  investigation  might 
bring  them  into  agreement;  this  would  have  a  physical 
meaning,  namely,  that  it  is  probably  a  change  in  the  con- 
dition of  the  erythrocytes  that  causes  the  increase  of  the 
reactivity  with  temperature. 

Two  other  haemolytic  substances  have  been  investigated 
by  the  same  authors,  namely,  the  oleate  of  sodium  and 
triolein.  They  gave,  with  the  same  suspension  of  erythro- 
cytes as  was  used  in  the  other  experiments,  namely  i  per 
cent  of  red  cells  from  the  horse,  the  following  results  :  — 
HAEMOLYSIS  BY  MEANS  OF 


o.oi  n.  SODIUM  OLEATE  (10  MIN.) 

o.oi  n.  TRIOLEIN  (15  MIN.) 

Temp. 

?obs. 

tfcalc. 

Temp. 

fate. 

(7calc. 

36.3 

0.125 

0.125 

38.9 

0.17 

0.17 

31-4 

O.I4 

O.I4 

35-7 

0.20 

0.20 

24.1 

0.18 

o.  16 

30.9 

0.32 

0.26 

15-9 

0.19 

0.19 

24.0 

0.40 

0.40 

12 

0.20 

0.21 

4 

0.25 

0.25 

^  =  3800 

n  =  1  3,800 

With  regard  to  the  magnitude  of  /*,  the  oleate  and  the 


VELOCITY  OF  REACTION.     HETEROGENEOUS  SYSTEMS     115 


triolein  seem  to  differ  from  the  other  lysins.  The  formula 
gives  the  observed  results  within  the  limits  of  the  errors 
of  observation. 

The  change  of  the  agglutinating  power  with  temperature 
was  investigated  in  an  analogous  manner.  The  values  for 
mercuric  chloride,  ricin,  coli-  and  typhoid-agglutinin  are 
given  below  for  the  shortest  times  used  :  — 

INFLUENCE  OF  TEMPERATURE  ON  AGGLUTINATION  BY  MEANS  OF 


o.i  n.  HgClj  (45  Mm.) 

RICIN  (30  MIN.) 

Temp. 

tfobs. 

?calc. 

Temp. 

tfobs. 

tfcalc. 

35-8 

0.085 

0.085 

36.2 

0.05 

0.05 

30.9 

O.IS 

0.15 

27.9 

0.12 

O.I  I 

25-9 

0.25 

0.24 

I5.6 

°-33     § 

o-37 

21.9 

o-55 

0.36 

IO.I 

0.70 

0.66 

16.1 

0.60 

0.65 

0.9 

1.30 

1.80 

12.3 

1.  00 

0.98 

^=17,900 

/t=  17,200 

COLI-AGGLUTININ    (lO   MlN.) 

TYPHOID-AGGLUTININ  (10  MIN.) 

Temp. 

?obi. 

ftalc. 

Temp. 

?obs. 

?calc. 

38.6 

0.005 

0.0043 

38.2 

0.002 

0.002 

34-9 

0.0055 

0.0072 

3I.I 

0.007 

0.0083 

30.9 

0.015 

0.0135 

27.4 

O.O2 

O.OlS 

24.9 

0.045 

0.042 

19.2 

0.13 

0.09 

21.2 

0.065 

0.068 

15.9 

0.20 

0.20 

I2.9 

0.30 

0.30 

"•5 

0-55 

°-55 

/i  =  3o,ioo 

/t=  37,200 

The  two  agglutinins  acting  upon  equine  erythrocytes 
give  remarkably  similar  values  of  /*,  although  the  time  of 
reaction  is  rather  long. 

The  values  of  /*  for  longer  times  seems  to  indicate 
that  the  limit-value  of  p  for  the  two  bacterio-agglutinins 


Il6  LECTURES  ON  IMMUNITY 

probably  differs  little  from  that  given  above.  They  are 
for  the  typhoid-agglutinin,  /^40  =  33,000,  /-t120  =  18,700,  and 
^180=8soo  (the  indices  represent  the  time  in  minutes). 
For  the  coli-agglutinin  there  are  two  different  series.  The 
one  proceeds  regularly,  so  that  p  sinks  with  increasing  time. 
In  the  other  series  an  irregularity  occurs ;  the  /rvalue  at 
first  sinks,  then  passes  through  a  minimum  and  thereafter 
through  a  maximum,  and  then  later  on  falls  toward  zero 
with  increasing  time.  The  two  series  were  carried  out 
with  the  same  preparations,  so  that  the  differences  may 
be  regarded  as  purely  accidental.  But  the  limit-value  /^0 
seems  to  be  nearly  the  same  in  the  two  series. 

The  phenomenon  of  agglutination  bears  a  great  simi- 
larity to  that  of  haemolysis  in  its  dependence  on  time  and 
temperature.  We  know  from  Eisenberg  and  Volk's  ex- 
periments that  the  absorption  of  the  agglutinins  reaches 
the  state  of  equilibrium  in  a  few  minutes  (less  than  5). 
But  still  the  agglutination  continues  through  hours,  espe- 
cially at  low  temperatures.  The  phenomenon  proceeds 
with  time  just  as  does  haemolysis,  although  the  haemolytic 
substance  is  absorbed  before  the  time  of  the  first  observa- 
tion. The  following  figures,  giving  the  quantity  of  coli- 
agglutinin  necessary  to  reach  the  observed  degree  of 
agglutination  at  36.6  and  12.3°  C,  may  illustrate  this 
peculiarity  :  — 

Time  (min.)  20  30  50  65  80  120 
(?  obs.  at  36.6  4  i  0.5  0.2  0.13  o.i 
(?  obs.  at  12.3  85  26  10  2  1.6  0.32 

The  figures  indicate  that  the  limit-value  for  infinite  time 
is  nearly  reached  in  120  minutes  at  the  higher  temperature, 
but  not  for  the  lower  one;  and  that  this  limit-value  is  of 


VELOCITY   OF  REACTION.      HETEROGENEOUS   SYSTEMS     1 1/ 


the  same  order  of  magnitude  (probably  equal)  in  the  two 
instances.  The  progress  of  agglutination  with  time  indi- 
cates that  after  the  agglutinin  has  been  absorbed  (in  the 
first  five  minutes)  some  change  (probably  coagulation) 
takes  place  slowly  within  the  bacteria,  which  thereby 
obtain  their  agglutinating  properties.  In  the  same  man- 
ner, after  a  haemolysin  has  been  very  rapidly  taken  up 
by  erythrocytes,  these  are  subject  to  a  slow  chemical 
change,  which  causes  them  to  give  up  their  colouring 
matter.  This  circumstance  seems  rather  incompatible 
with  the  commonly  adopted  idea  that  the  agglutination 
might  depend  upon  some  electric  charge  of  the  bacteria, 
due  to  the  absorption  of  the  agglutinin,  since  the  electric 
charge  very  likely  follows  immediately  upon  the  absorp- 
tion of  agglutinin. 

These  far-reaching  investigations  of  Madsen  and  his 
pupils  have  also  made  us  familiar  with  some  substances, 
the  action  of  which  increases  with  sinking  temperature, 
or  has  a  maximum  or  minimum  at  a  certain  temperature. 

H^EMOLYTIC  ACTION  AT  DIFFERENT  TEMPERATURES 


POISON  OF  WATER-MOCCASIN 

COBRA  POISON 

STAPHYLOLYSIN 

Time,  5  min. 

Time,  15  min. 

Time,  15  min. 

Time,  15  min. 

Time,  45  min. 

Temp. 

?obs. 

Temp. 

?obs. 

Temp. 

?obs. 

Temp. 

fobs. 

Temp. 

?oba. 

39-3 

0.38 

39-3 

0.28 

37-3 

0.225 

36.5 

0-35 

36.4 

0-35 

35-2 

0.36 

35-2 

0.28 

30.8 

0.25 

29.1 

0.17 

28.6 

0.08 

30-7 

0-35 

30-7 

0-3 

24.1 

0.30 

24-3 

0.23 

24.4 

0.07 

28.2 

0-35 

28.2 

0-33 

17.7 

0.30 

19.5 

0.33 

19.7 

0.075 

19.2 

°-3 

19.2 

o-3 

14.2 

0.25 

I3.6 

1.8 

"•3 

0.6 

14.8 

o-3 

14.8 

0.25 

10.8 

0.25 

10.6 

0.25 

10.6 

0.23 

Il8  LECTURES  ON  IMMUNITY 

As  illustrations  may  be  given  the  haemolytic  action  of 
the  snake-venoms  of  the  water-moccasin  (Amis  trod  on 
piscivorus),  and  cobra  (Naja  tripudians)  and  of  staphy- 
lolysin,  produced  by  staphylococcus. 

The  snake-poisons  were  tested  on  horse-blood,  the 
staphylolysin  on  rabbit-blood.  Probably  the  observed 
phenomenon  is  of  complex  nature.  A  maximum  effect 
might  result  if  the  haemolytic  agent  were  decomposed 
with  increasing  temperature.  At  low  temperatures,  then, 
where  the  decomposition  is  insignificant,  the  poisons  be- 
have normally,  the  velocity  of  reaction  increases  with  tem- 
perature. If  then  at  higher  temperatures  the  decompo- 
sition or  dissociation  of  the^  poisonous  substance  increases 
more  rapidly  with  temperature  than  the  velocity  of  the 
real  reaction,  then  the  quantity  of  poison  necessary  for  a 
given  haemolytic  effect  (in  a  given  time)  must  increase  with 
temperature.  A  closer  investigation  of  these  complicated 
phenomena  will  be  necessary  to  show  whether  an  explana- 
tion analogous  to  that  sketched  above  may  be  assumed. 

The  phenomena  studied  above  in  this  chapter  are,  gen- 
erally speaking,  due  as  well  to  velocities  of  reaction  as  to 
real  chemical  equilibria.  These  prevail  the  more,  the 
longer  the  time  of  reaction  and  the  higher  the  tempera- 
ture. The  observations  have  great  importance  because 
they  correspond  to  the  method  of  working  actually  used, 
which  is  determined  by  the  nature  of  the  material  em- 
ployed. Hence  their  discussion  is  useful  for  the  compre- 
hension of  the  results  of  the  ordinary  method  of  working, 
and  for  the  arrangement  of  similar  experiments.  There- 
fore I  have  discussed  them  in  a  rather  detailed  manner, 
although  their  theoretical  meaning  is  not  very  simple. 


VELOCITY  OF   REACTION.      HETEROGENEOUS  SYSTEMS     1 19 

Rather  similar  to  these  haemolytic  and  agglutinating 
processes  in  which  the  chemical  attack  is  directed  against 
cells  suspended  in  the  acting  medium,  are  some  other 
processes  in  heterogeneous  systems,  namely,  the  decom- 
position of  coagulated  protein,  or  of  small  emulsified 
fat  drops  by  so-called  Upases.  These  processes  are  not 
very  different  from  those  in  homogeneous  systems.  The 
coagulated  proteins  are  introduced  in  the  state  of  a  fine 
powder  and  the  suspension  held  in  uniform  concentration 
in  all  its  parts  by  shaking.  In  this  manner  the  digestion 
of  coagulated  egg-white  by  means  of  pepsin  (Sjoqvist) 
or  for  the  digestion  of  casein  by  means  of  trypsin  (Madsen 
and  Walbum)  have  been  examined. 

Perhaps  the  most  important  of  the  processes  is  the  diges- 
tion of  coagulated  albumen  by  pepsin  (in  the  presence  of 
acids).  Regarding  this  process  Schutz  *  had  found  the 
rule,  that  the  digested  quantity  of  albumen  hydrolysed  in 
a  given  time  is  proportional  to  the  square  root  of  the  time 
and  of  the  concentration  of  pepsin.  Against  the  figures 
of  Schutz,  which,  according  to  a  criticism  of  Sawjalow,2 
give  no  very  accurate  results,  he  quotes  the  experiment 
of  Sjoqvist3  as  indicating  that  the  reaction  is  proportional 
to  the  time,  i.e.  follows  the  laws  for  a  monomolecular 
reaction.  In  Sjoqvist's  experiment  the  protein  was  coagu- 
lated egg-albumen  in  the  state  of  a  powder,  which  was 
brought  in  100  c.c.  of  a  solution  at  37°  C.  containing 
50  c.c.  of  o.i  n.  hydrochloric  acid,  2.5,  5,  10,  or  20  c.c. 
of  a  0.067  per  cent  solution  of  pepsin  and  water  to  con- 

1Schiitz:  Zeitschr.f.  ph.  ch.  v.  Hoppe-Scyler,  9.  557  (1885). 
2 Sawjalow:   Zeitschr.  / ph.  ch.  v.  Ifoppe-Seyler,$Q.  307  (1905). 
3 Sjoqvist:  Skand.  Archiv.  f.  Physiologic,  5.  (1895). 


120 


LECTURES  ON  IMMUNITY 


stant  volumes.  After  a  certain  time  ( i  to  20  hours)  a  sample 
of  the  solution  was  cooled  to  o°  C.,  the  albumen  was  cen- 
trifugalised,  and  the  content  of  nitrogen  in  the  liquid 
determined  according  to  the  method  of  Kjeldahl. 

In  this  manner  the  digestion  was  followed.  Sjoqvist 
found  that  the  same  quantity  (<2)  is  digested  if  the  time 
(/)  of  digestion  is  inversely  proportional  to  the  concentra- 
tion (c)  of  the  pepsin,  as  is  shown  by  the  following  figures  : 


c 

t  (hours) 

Q 

o-5 

16 

6.90 

i 

3 

6.70 

2 

4 

6.77 

4 

2 

7.00 

During  the  first  time  there  are  some  deviations.     The 
progress  with  time  is  indicated  by  the  following  figures 


t  (hours) 

?obs. 

tfcalc.l 

?calc.2 

o-5 

2.25 

3-14 

2.18 

i 

3-16 

3-47 

3.00 

2 

4.08 

4.08 

4.04 

3 

4.72 

4.64 

4.78 

4 

5-24 

S-'S 

5-35 

6 

6.  10 

6.04 

6.21 

8 

6.84 

6.77 

6.84 

10 

7-38 

7-39 

7-35 

12 

7.84 

7.90 

7.76 

16 

8.54 

8.67 

8-39 

20 

8.94 

9.21 

8.83 

30 

9-39 

9-93 

9-43 

40 

9.85 

10.21 

9.90 

oo 

10.40 

(10.40) 

(10.40) 

The  calculated  figures  <2calc>1  are  found  from  the  com- 
mon formula  for  the  monomolecular  reaction,  those  signed 
£^.2  from  the  formula  given  above  for  the  digestion  of 


VELOCITY  OF  REACTION.      HETEROGENEOUS  SYSTEMS     121 

dissolved  egg-albumen.  As  will  be  seen,  the  latter  formula 
agrees  very  closely  with  the  experiments,  and  much  better 
than  the  common  formula  for  monomolecular  reactions. 
This  indicates  that  the  digestion  follows  the  same  laws  in 
both  cases. 

In  experiments  on  digestion  there  is  often  used  a 
method  of  including  the  coagulated  albumen  in  short 
capillary  tubes,  so-called  tubes  of  Mett.  By  the  aid  of 
this  method  Borissow  found  the  rule  of  Schiitz  to  be 
valid,  if  a  solution  of  acid  and  pepsin  diffused  into  the 
tubes ;  whereas  Sawjalow,  who  mixed  the  pepsin  with  the 
albumen,  found  then  that  the  height  of  the  digested  albu- 
men-pillar was  proportional  to  the  quantity  of  pepsin,  and 
not  to  the  square  root  of  it,  as  Borissow  had  found. 
As  is  seen  above,  the  results  of  Sjoqvist  agree  in  the  most 
satisfactory  manner  with  the  values  <2calc.2,  which  for  short 
times  coincide  with  values  calculated  from  Schiitz's  rule. 
It  should  be  emphasised  that  experiments  with  Mett's 
tubes  ought  not  to  be  used  in  investigating  these  questions. 
For  in  them  the  rate  of  diffusion  interferes  with  the  chem- 
ical reaction,  and  if  it  is  the  slower  of  these  processes, 
it  causes  the  digestion  to  proceed  proportionately  to  the 
square  root  of  the  time  and  concentration.  An  analogous 
experiment  may  be  made  with  diffusion  of  alkali  into  a 
Mett's  tube  filled  with  an  acidulated  jelly  solution  plus 
phenolphthalein.  At  a  given  time  (/)  the  concentration 
of  alkali  in  the  Mett's  tube  surrounded  by  a  solution  of 
the  concentration  2  is  at  a  given  point  double  as  great  as 
at  the  corresponding  point  in  a  Mett's  tube  surrounded  by 
an  alkaline  solution  of  the  concentration  i .  Now  the  height 
to  which  the  alkali  in  a  given  concentration  has  reached 


122 


LECTURES  ON  IMMUNITY 


after  a  certain  time  (/)  is  proportional  to  its  square  root. 
Therefore  at  the  time  — —  the  distribution  of  alkali  in  the 

V2 

first  tube  is  nearly  the  same  as  the  distribution  of  alkali 
in  the  second  tube  after  the  time  /.  This  may  be  seen  in 
the  height  of  the  pink-coloured  column  of  jelly  which  is 
the  same  in  the  two  cases.  Experiments  with  the  diffu- 
sion of  pepsin  are  of  quite  the  same  type.  The  indicator 
is  in  this  case  not  the  reddening  phenolphthalein,  but  the 
liquefying  solution  of  albumen.  —  One  measures  the  length 
of  the  liquefied  albumen-pillar  at  a  given  time.  —  Therefore 
Pawlow's  and  Borissow's  experiments,  which  indicate  that 
the  liquefaction  of  coagulated  albumen  or  gelatin  goes  on 
proportionally  to  the  square  root  of  time  or  of  reacting 
enzyme  (pepsin,  trypsin,  etc.),  are  not  conclusive  in  favour 
of  Schiitz's  rule. 

A  process  which  is  very  analogous  to  the  digestion  of 
egg-white  is  that  of  the  saponification  of  fats  by  means  of 
gastric  juice  or  of  extracts  of  gastric  tissues  (steapsin). 
Volhard l  used  glycerine  extracts  of  the  pig's  stomach  and 
observed  that  the  quotient,  q :  V/=  ^>  of  the  digested 
quantity  q  (in  per  cent),  and  the  square  root  of  the 
concentration  of  steapsin,  /,  is  nearly  constant.  This  ob- 


GLYCERINE  EXTRACT  (24  HOURS) 

GASTRIC  JUICE  (i  HOURJ 

/ 

? 

k 

/ 

? 

k 

i 

4-7 

4-7 

i 

4.1 

4.1 

4 

8.5 

4-3 

4 

II.  2 

5.6 

9 

15.0 

5-° 

9 

17-3 

5.8 

16 

19-5 

4.9 

16 

21.3 

5-3 

25 

24-5 

4.9 

1  Volhard ".  Ztitschr.f.  klin.  Medicin,  42.  414,  and  43.  397  (1901). 


VELOCITY  OF  REACTION.     HETEROGENEOUS  SYSTEMS     123 


servation  was  confirmed  by  Stade,1  as  may  be  seen  from 
the  above  figures  (temp.  40°). 

If  the  digestion  proceeds  further  than  25  per  cent  the 
rule  of  Schiitz  is  no  longer  applicable.  We  then  may  use 
the  general  formula  (p.  64)  as  is  seen  by  the  next  figures 
valid  for  digestion  by  gastric  juice  during  16  hours  at 
40°  C.  (.AT/*  =27):  — 


/ 

fobs. 

fMfc 

I 

21.6 

21.6 

4 

40.7 

39-6 

9 

50-9 

54-6 

16 

674 

66.7 

Stade  has  further  done  a  series  of  measurements  of  the 
progress  of  saponification  of  an  emulsion  of  the  fat  from  the 
yolk  of  egg  by  neutralised  gastric  juice.  These  measure- 
ments follow  nearly  the  same  formula  as  those  of  Sjoqvist, 
as  may  be  seen  from  the  calculated  values. 
PROGRESS  OF  SAPONIFICATION  OF  YOLK  OF  EGG  BY  MEANS  OF  GASTRIC  JUICE 


TIME 
(hours) 

fobs. 

tfcalc. 

TIME 
(hours) 

?ObB. 

fcalc. 

2 

20.4 

1  8.6 

12 

24.1 

24.5 

4 

25.6 

257 

16 

254 

27.9 

6 

29.8 

30-8 

21* 

28.5 

314 

8 

35-3 

34-8 

37* 

39.5 

40.0 

10 

37-6 

38.3 

39* 

39-8 

40.9 

25* 

49-5 

55-2 

43* 

41.7 

42.6 

29* 

5i.5 

58.2 

46 

46.2 

43-8 

31* 

554 

59-6 

65 

53-6 

50.2 

35* 

60.9 

62.0 

75 

77-5 

78.4 

1  Stade :  Hofmtistcrs  Beitr'dge,  3.  291  (1902).     The  dates  with  an  asterisk 
are  the  means  of  two  measurements. 


124 


LECTURES  ON  IMMUNITY 


The  constants,  KP,  are  respectively  10  and  3.  For  short 
times  the  digested  quantity  is  proportional  to  the  square  root 
of  the  time,  so  that  if  as  well  time,  t,  as  quantity,/  of  steapsin 
change,  the  digested  quantity  is  proportional  to  the  square- 
root  of  the  product  of  f- 1.  Even  this  rule  has  been  verified 
by  Stade.  Stade's  work  has  been  repeated  by  Engel1  for 
the  glycerine  extract  of  "  pancreatin  Rhenania  "  as  well  as 
for  gastric  juice,  acting  on  an  emulsion  of  egg-yolk.  The 
following  figures  reproduce  two  series  of  observations,  the 
one  at  30°,  the  other  at  40°  with  1.24  times  as  much  extract 
of  pancreatin.  The  time  of  digestion  was  6  and  18  hours 
respectively.  From  these  observations  we  may  calculate 
the  variation  of  K  with  temperature.  We  so  find  /JL  = 
15,600. 


t=  30°  C. 

/  =  40°  C. 

/-I 

A>bs.  =  4-7 

Aalc.  =  5  ° 

/=  1.24 

A>bs.=  12.8 

Aalc.=  *4-i 

4 

IO 

9.8 

4.96 

24.7 

26.8 

9 

15 

14.6 

ii.  16 

39-5 

38.2 

16 

19-5 

IQ.O 

19.84 

51.6 

48.2 

25 

22.3 

23.4 

31.0 

59-5 

57-i 

36 

24.4 

27.6 

44.64 

63.1 

64.8 

^  =  1.3:6 

JT=  8.9:18 

Stade  has  furnished  some  measurements  on  the  in- 
fluence of  the  concentration  (c)  of  gastric  juice  at  40° 
C.  on  this  process,  which  we  reproduce  below.  The  tabu- 
lated figures  concern  the  hydrolysed  quantity  in  per  cent 


1  Engel:  Hofmeisters  Beitrage,  7-  77  (1905), 


VELOCITY  OF  REACTION.  HETEROGENEOUS  SYSTEMS  125 


TIM  EOF  ACTION 

TIME  OF 
ACTION 

TIME  OF 
ACTION 

TIME  OF 
ACTION 

TIME  OF 
ACTION 

i  HOUR 

4  HOURS 

9  HOURS 

16  HOURS 

25  HOURS 

c 

Abs. 

Aalc. 

Abs. 

Aalc. 

Abs. 

Aalc- 

Abs. 

Aalc. 

Abs. 

Aalc. 

I 

4.1 

6.2 

13.7 

I2.I 

19.2 

I7.8 

21.6 

23.2 

31-5 

28.4 

4 

II.  2 

I2.I 

28.0 

23.2 

39-8 

33-3 

40.7 

42.5 

46.0 

5°-7 

9 

17-3 

I7.8 

38.9 

33-3 

494 

46.7 

5°-9 

58.0 

65.6 

67.6 

16 

21.3 

23.2 

44.0 

42.5 

52.9 

58.0 

57-4 

70.3 

73-6 

79.6 

25 

23.6 

28.4 

45-4 

50-7 

63.3 

67.6 

68.4 

79.6 

74.1 

88.1 

If  we  calculate  the  constants  for  the  five  series,  we 
find:  — 

1.8      10.7      21  27  and     41      or 

1.1,8     4.2,7     9.2,3     16.1,7     and     25.1,64 

or  in  mean  the  constant  is  2  t.  With  this  constant  the 
calculated  figures  are  obtained.  The  observed  values 
agree  in  general  as  well  as  might  be  expected  with  the 
calculated  ones,  and  probably  the  deviation  is  not  greater 
than  might  be  referred  to  the  experimental  errors.  (Per- 
haps real  or  so-called  false  equilibria  disturb  the  observa- 
tions for  high  values  of  /.) 

The  seeds  of  Ricinns  communis  (castor  bean)  contain  an 
enzyme  which  decomposes  the  oil  from  these  seeds  into 
fatty  acid  and  glycerine.  This  process  seems  also  to 
follow  the  same  laws  as  the  decomposition  of  fats  by 
gastric  juice.  I  reproduce  some  figures  from  the  article 
of  Connstein,  Hoyer,  and  Wartenberg.1  They  prepared 
an  emulsion  by  grinding  5  g.  of  Ricinus  seeds  and  6.5  g. 
of  castor  oil,  and  thereafter  adding  4  g.  of  an  acid.  The 

1  Connstein,  Hoyer,  and  Wartenberg:  BerichU  d.  d.  chtm.  Gcs.,  35.  3988 
(1903). 


126 


LECTURES  ON  IMMUNITY 


emulsion  was  held  at  constant  temperature  and  at  given 
times  samples  were  removed  and  titrated  for  their  free 
acid.  (The  acid  initially  added  was  subtracted.)  The 
first  figures  concern  an  emulsion  in  o.  I  n.  sulphuric  acid, 
the  later  figures  are  found  for  emulsions  in  o.i  and  0.4  n. 
acetic  acid. 


SULPHURIC  ACID  o.i  N. 

ACETIC  ACID  o.i  N. 

ACETIC  ACID  0.4  N. 

Time  (min.) 

A>bs. 

Aalc. 

Time  (hr.) 

Abs. 

Aalc. 

Time(hr.) 

A>bs. 

/calc. 

15 

12 

20 

I 

50 

48.6 

I 

65 

63-9 

30 

20 

27 

2 

65 

62.8 

2 

86 

78.8 

45 

30 

32 

3 

70 

7*-S 

3 

84 

86.5 

60 

33 

36 

4 

72 

77.6 

4 

84 

91.2 

90 

4i 

43 

24 

8o(?) 

99-5 

24 

9i(?) 

99.9 

15° 

54 

53 

210 

59 

59 

330 

68 

69 

1620 

8i(?) 

97 

The  constants  are  1.47  for  the  first,  180  and  380  respec- 
tively for  the  later  experiments. 

The  deviation  of  the  figures  for  the  later  times  seems  to 
indicate  that  we  have  here  to  do  with  either  real  equilibria 
in  the  presence  of  lipases  acting  on  ethylic  butyrate,  mono- 
glycerid  of  butyric  acid,  and  triacetin,  and  known  from 
Kastle  and  Loewenhart's,  Hanriot's,  and  A.  E.  Taylor's  in- 
vestigations,1 or  some  perhaps  false  equilibrium.  These  are 
very  common  with  enzymes,  as  Tammann  (I.e.)  found. 
Even  the  figures  for  less  than  45  minutes  indicate  a  devia- 
tion from  the  premises  of  the  calculation.  There  are  also 


1  Kastle  and  Loewenhart :  Amer.  Chem.  Journ.,  24.  491  (1900)  ;   Hanriot, 
C.  R.t  132.  212  (1901);  A.  E. Taylor:  Journ.  Biol.  Chemistry,  2.  87  (1906). 


VELOCITY  OF  REACTION.      HETEROGENEOUS   SYSTEMS     127 


some  observations  regarding  the  influence  of  the  quantity 
of  enzyme.  With  0.5  g.  of  Ricinus  seed  were  emulsified 
5,  10,  15,  20,  25,  or  50  g.  of  Ricinus  oil  and  the  same 
quantities  of  2  per  cent  acetic  acid.  The  results  are 
indicated  in  the  table  below.  The  calculated  figures  are 
found  under  the  assumption  that  the  acting  mass  of  the 
enzyme  is  proportional  to  its  quantity.  The  agreement  be- 
tween calculated  and  observed  values  is  very  satisfactory, 
except  for  the  greatest  quantities.  The  constant  for  two 
days  is,  within  the  errors  of  observation,  double  that  for 
one  day.  The  concentration  in  the  presence  of  50  g. 
oil  and  50  g.  acid  is  taken  as  unit. 

ACTION  OF  0.5  G.  RICINUS  SEEDS  ON  DIFFERENT  QUANTITIES  OF  RICINUS 

OIL 


AFTER  i  DAY 

AFTER  2  DAYS 

Oil 

Acid 

Ab.. 

>calc. 

A>b8. 

Aalc. 

50 

5° 

49 

49 

49 

59 

25 

25 

60 

63 

74 

74 

20 

2O 

7' 

69 

80 

78 

15 

IS 

77 

75 

87 

84 

10 

10 

81 

83 

86 

9i 

5 

5 

89 

94 

92 

98 

KP  =  186 

KP=  300 

In  this  case  the  presence  of  a  certain  quantity  of  free 
acid,  about  4  c.c.  of  a  0.2  normal  solution,  the  same 
quantity  for  all  acids,  weak  or  strong,  is  necessary.  This 
circumstance  resembles  very  closely  the  action  of  acids 
in  peptic  digestion.  If  no  acid  is  added,  the  acid  in  the 
seeds  acts,  and  new  acid  is  procured  by  the  process. 

A  lipolytic  process,  which  probably  should  be  regarded 
as  occurring  in  a  homogeneous  system,  is  that  studied  by 


128  LECTURES  ON  IMMUNITY 

Zeller  l  on  the  lipolytic  agent  in  the  mushroom  (Amanita 
muscarid).  An  aqueous  extract  of  the  powder  of  this  mush- 
room had  no  lipolytic  action.  But  if  the  powder  were  mixed 
with  olive  oil  or  tallow,  they  were  slowly  decomposed.  I 
reproduce  some  figures  for  olive  oil.  In  this  case  the  reac- 
tion is  decidedly  monomolecular  (the  constant  used  for  the 
calculation  is  0.00045).  The  acid  from  the  olive  oil  evi- 
dently has  no  sensible  influence  on  the  enzyme. 

Time  (hours)  48          118          160         304         485          631 

Decomposition  (per  cent)  4.8  11.5  14.2  28.5  38.9  46.3 
Decomposition  (calc.)  4.8  10.9  15.3  27.0  39.5  48.0 

Regarding  the  lipolytic  action  of  the  cytoplasma  of  the 
seeds  of  Ricinus  commtmis,  a  large  number  of  experi- 
ments have  been  carried  out  by  Nicloux.2  He  found  that 
the  catalytic  agent  is  not  soluble  in  water,  which  seems 
to  arrest  its  action.  The  conditions  of  the  reaction  seem, 
therefore,  to  have  been  nearly  the  same  as  in  the  ex- 
periments of  Zeller.  The  reaction  proceeds  (at  low  tem- 
peratures) very  closely  according  to  the  law  valid  for 
monomolecular  reactions.  The  cytoplasma  was  suspended 
in  the  oil  examined,  in  most  cases  cotton  oil,  and  thereafter 
water  containing  a  small  quantity  of  acetic  acid  was  added. 
The  following  figures,  valid  for  18°  C.,  indicate  that  the 
process  is  monomolecular  :  — 

Time  (min.)  30       45        60       90       127      150      210     450 

Saponification,  per  cent  (.*•)  23.6     33.1     40.4     54.8     67.0     73.2     85.5     94.4 

K=—  log  IOQ  _  x  0.388  0.387  0.375  °-382  °-392  0.381  0.399  0-278 

1  Zeller :   Sitz.  ber.  d.  Ak.  d.  Wiss,  zu  Wien  (chemical  memoirs  =  Monat- 
shefte  fur  Chemie),  36.   727  (1905). 

2  M.  Nicloux:   C.  R.  de  la  Soc  de.  Biol.  56.  I.  701,  702,  839,  840,  and  868 
(1904). 


VELOCITY   OF   REACTION.      HETEROGENEOUS   SYSTEMS      129 

At  higher  temperatures,  above  25°  C.,  the  constant  K 
decreases  during  the  period  of  reaction,  as  will  be  seen 
from  the  following  figures,  which  give  the  mean  values  of 
K.icr*  during  the  time  intervals  30-90  and  90-180  min- 
utes. From  these  an  extrapolated  value  for  the  time  o,  the 
beginning  of  the  reaction,  is  calculated  :  — 

Temp.                              5  10        15  20  25  30  35  40  45 

o  min.  7.7  12.5  14.6  20.6  26.6  30.3  40.1  34.4  27.2 

30-90  min.  9.0  12.6  13.7  19.3  24.2  26.6  29.7  19.2  10.5 

90-180  min.  6.3  12.4  15.4  21.9  21.5  22.6  20.4       9.1       3.2 


60 — -.- —  —       —        —       —      0.041  0.057  0.130  0*259  0.413 

K  has  a  maximum  at  about  37°  C.  This  evidently  depends 
upon  the  rapid  destruction  of  the  catalytic  agent  at  higher 
temperatures.  Nicloux  has  found  that  at  55°  C.  its  action 
is  totally  nullified  in  ten  minutes.  This  destruction  is 
measured  by  the  decrease  of  log  K  during  the  progress  of 
the  saponification,  if  the  process  is  monomolecular,  as 
indicated  by  the  values  found  at  lower  temperatures.  At 
temperatures  below  2 5°  C.  this  decrease  is  insensible;  at 
higher  temperatures  the  destruction  of  the  enzyme  proceeds 
at  about  double  the  speed  with  increase  of  the  temper- 
ature of  5°  C.  This  corresponds  to  a  value  of  p  = 
26,000. 

The  extrapolated  value  of  K  itself  at  the  time  o  shows 
a  remarkably  small  increase  with  temperature.  An  increase 
of  about  14°  C.  is  necessary  to  increase  it  in  the  proportion 
2  to  i.  The  value  of  p  calculated  from  the  figures  for  10° 
and  30°  C.  is  only  7540. 

This  investigation  affords  a  good  insight  into  the  real 
meaning  of  optima.  If  we  regard  the  time  o,  the  optimum 


130  LECTURES  ON  IMMUNITY 

seems  to  occur  at  about  37°  C.  In  the  interval,  30-90 
min.,  the  optimum  seems  to  lie  at  about  33°  C.,  and  in  the 
interval  90-180  min.  at  about  29°  C.  The  position  of  the 
optimum  evidently  depends  on  how  rapidly  the  experi- 
mental manipulations  are  done.  If  it  were  possible  to 
examine  K  immediately  after  mixing  the  reagents,  the 
optimum  would  probably  be  found  to  lie  at  a  much  higher 
temperature;  or  there  would  perhaps  be  no  optimum  at 
all. 

It  is  worthy  of  mention  that  the  dry  cytoplasma  sus- 
pended in  pure  oil  resists  a  temperature  of  100°  C.  for 
twenty  hours ;  at  120°  C.  its  activity  decreases  one-third  in 
a  quarter  of  an  hour. 

Quite  recently  A.  E.  Taylor1  has  carried  out  an  investi- 
gation on  the  action  of  the  lipase  from  the  castor  bean  on 
the  triglycerid  of  acetic  acid,  commonly  termed  triacetin. 
This  compound  is  rather  soluble  in  water,  so  that  homoge- 
neous solutions  were  prepared  containing  0.5,  I,  or  2  per 
cent  (up  to  3  per  cent)  of  triacetin  together  with  i  g.  of  the 
powder  of  castor  beans,  from  which  the  fat  had  been 
extracted,  in  looc.c.  of  water.  The  following  values 
were  obtained,  indicating  a  monomolecular  process.  The 

I             A. 
velocity-constant  is  K  =-  log •  io4- 

t  ./JL  —~  X 

The  agreement  between  the  three  values  of  K  indicates 
that  the  decomposed  quantity  is  very  closely  proportional 
to  the  quantity  of  the  substrate.  The  regularity  of  this 
process  is  evidently  higher  than  that  of  any  other  ferment- 
ative action  hitherto  studied.  The  velocity  of  reaction  in- 
creased in  the  proportion  of  i  to  2.6  if  the  temperature 

1  A.  E.  Taylor:  Journ.  Biol.  Chemistry,  2.  87  (1906). 


VELOCITY  OF  REACTION.     HETEROGENEOUS  SYSTEMS     l$t 


was  elevated  from  18°  C.  to  28°  C.     This  corresponds  to  a 
value  for  p  of  16,700. 

SAPONIFICATION  OF  TRIACETIN  BY  MEANS  OF  LIPASE  FROM  THE  CASTOR 
BEAN  AT  i8°C.  (A.  E.TAYLOR) 


/  (hours) 

0.5  PER  CENT 

I  PER  CENT 

2  PER  CENT 

A  -X 

K 

A  -  X 

K 

A  -  X 

K 

O 

100 

— 

100 

— 

100 

— 

4 

90.4 

109 

91.7 

94 

90.2 

112 

8 

83.8 

96 

82.6 

104 

82.6 

104 

16 

71-3 

92 

66.2 

112 

67.7 

1  06 

24 

58.2 

98 

58.2 

98 

56.9 

102 

28 

51-1 

104 

51.2 

104 

49.8 

108 

32 

52-3 

88 

45-8 

1  06 

51-5 

90 

40 

37-7 

106 

39-1 

102 

40.5 

98 

48 

34-8 

97 

34-5 

96 

36.4 

9i 

Mean      99              102              101 

Taylor  thereafter  investigated  a  suspension  of  triolein 
(2  per  cent)  in  water  containing  I  g.  of  castor  bean 
powder  in  100  c.c.  The  liquid  was  shaken  vigorously. 
He  found  the  following  values  of  A  —  x  for  the  days, 
termed  t. 

SAPONIFICATION  OF  A  2  PER  CENT  EMULSION  OF  TRIOLEIN  AT  i8°C.  BY 
LIPASE  FROM  THE  CASTOR  BEAN  (TAYLOR) 

/  (days)          012  3457          9111518 

A—x  loo      97      95      92.5    91      89      84      78.4    72.8    66.9    61.9 

x:t  —         3      2.5         2.5    2.3     2.2      2.3         2.4      2.5       2.4      2.1 

Here  evidently  the  transformed  quantity  (x)  is,  as  the 
last  line  indicates,  proportional  to  the  time.  This  is  easily 
explained.  Through  the  strong  shaking  the  water  is  a 
concentrated  solution  of  triolein,  its  content  of  triolein  is 
constant,  independent  of  time.  Therefore,  as  the  concen- 


132  LECTURES  ON  IMMUNITY 

tration  of  the  ferment  is  also  unaltered  in  time,  the  quan- 
tity of  triolein  decomposed  in  the  unit  of  time  is  constant, 
and  the  total  quantity  proportional  to  the  time  of  reaction. 
We  might  perhaps  at  first  expect,  with  Taylor,  that  the 
velocity  of  reaction  might  increase  about  in  the  proportion 
1:2.6  for  an  increase  of  10°  in  temperature;  instead  of 
this  Taylor  found  the  proportion  1:1.2.  This  will  be  easily 
understood  if  the  solubility  of  the  triolein  diminishes  in 
about  the  proportion  i  :  2.2  for  an  elevation  of  10°  C.  The 
velocity  of  reaction  will  then  increase  in  the  proportion 

2.6 
i: — =1:1.2,  as  found  by   Taylor.     Taylor's  conclusion 

from  the  low  value  1.2  that  we  do  not  observe  a  velocity  of 
reaction  but  of  some  other 'process,  such  as  diffusion,  seems 
not  very  convincing. 

Kastle  and  Loewenhart1  had  already  (1900)  found  that 
the  velocity  of  reaction  of  monobutrinwith  animal  lipase  is 
proportional  to  the  concentration  of  the  ferment. 

Here  we  observe  evidently  a  very  simple  monomolecular 
process.  New  investigations  on  the  different  results  of 
Connstein,  Hoyer,  and  Wartenberg  seem  therefore  very 
desirable. 

Taylor  found  that  the  process  is  reversible,  the  ester  may 
be  formed  from  glycerine  and  fatty  acid  under  the  influence 
of  the  lipase.  The  equilibrium  is  reached  very  slowly  and 
does  not  differ  sensibly  from  that  attained  under  the  influ- 
ence of  an  acid.  The  following  end-values  were  obtained 
by  means  of  normal  sulphuric  acid  and  lipase  (after 
several  months):  — 

1  Kastle  and  Loewenhart  :  Amer.  Chem.  Journ.  24.  491  (1900),  as  cited 
by  Taylor. 


VELOCITY  OF  REACTION.     HETEROGENEOUS  SYSTEMS     133 
EQUILIBRIUM  IN   SOLUTION  OF  TRIACETIN  AT  i8°C.  (A.  E.  TAYLOR) 


CONCENTRATION 

HYDROLYSIS  BY  MEANS  OF 

per  cent 

H2S04 

Lipase 

Calc. 

o-5 

88 

86 

88 

I.O 

82 

79 

80.  i 

2.0 

78 

70 

69.8 

The  calculated  values  are  found  according  to  the  law  of 
Guldberg  and  Waage,  under  the  assumption  that  the  first 
figure  (88)  is  correct.  As  will  be  seen,  the  figures  found  for 
the  action  of  lipase  agree  better  with  the  theory  than  those 
for  the  catalytic  action  of  the  sulphuric  acid.  As  probably 
the  same  end-value  is  reached,  be  the  catalytic  agent  sul- 
phuric acid  or  lipase,  we  conclude  that  the  spontaneous 
hydrolysis  of  triacetin  would  reach  the  same  end-  value, 
and  that  the  catalysor  only  accelerates  the  process,  as  is 
generally  assumed  and  especially  set  forth  by  Ostwald. 

This  circumstance,  that  equilibria  are  reached  under  the 
action  of  ferments,  so  that  the  reaction  may  be  carried  in 
the  one  or  in  the  other  direction,  is  a  direct  illustration  of 
the  fact  that  we  may  apply  the  laws  of  physical  chemistry 
to  biological  science.  The  first  discovery  that  ferments 
may  synthetise  as  well  as  decompose  was  made  by  Hill  l  in 
1898  and  excited  a  very  great  interest.  He  found  that  it 
is  possible  to  synthetise  a  maltose  (according  to  Emmer- 
ling,2  it  is  an  isomaltose)  from  glucose  by  means  of  yeast, 
according  to  the  formula  :  — 


2  C6H1206 


C12H22On 


H20. 


1  Hill:  Journ.  Chem.  Soc.t  73.  643  (1898). 

2  Taylor:  University  of  California  Publications,  Pathology,  Vol.  I.,  33  and 
65  (1904).     For  references  on  literature  see  this  last  memoir. 


134  LECTURES  ON  IMMUNITY 

The  sign  -^  indicates  that  the  decomposition  of  the  di- 
saccharide  by  means  of  yeast  is  also  possible,  and  this  is 
the  normal  process.  In  a  similar  manner  it  is  possible  to 
reverse  this  reaction  under  the  influence  of  sulphuric  acid 
as  the  catalysor,  as  was  shown  by  Musculus,  Wohl,  and 
Fischer. 

Fischer  and  Armstrong  synthetised  isolactose  by  means 
of  kephir  yeast  (lactase)  from  //-glucose  and  ^/-galactose. 

Kastle  and  Loewenhart,  as  well  as  Hanriot,  accomplished 
the  synthesis  of  ethyl  and  monoglyceryl  butyrate  by  means 
of  animal  lipase ;  and  Taylor  synthetised  olein-triglycerid 
by  means  of  lipase  from  the  castor  bean,  but  he  did  not  suc- 
ceed in  reversing  tryptic  digestion.1  Emmerling  added  a 
maltase  from  yeast  to  a  mixture  of  glucose  and  nitril  man- 
del  glucoside  and  recovered  amygdalin  after  the  lapse 
of  three  months.  As  is  seen  from  these  illustrations,  the 
reversibility  of  processes  accelerated  by  ferments  is  a 
normal  phenomenon. 

All  the  experiments  cited  which  give  a  constant  value 
of  qt  seem  to  indicate  that  even  here  the  reagents  dif- 
fuse into  the  small  particles  of  the  substance  examined 
with  such  a  speed  that  the  time  of  diffusion  may  be  re- 
garded as  very  low  compared  with  the  time  of  reaction. 
For  the  erythrocytes  and  bacteria  this  may  be  easily  under- 
stood, because  their  linear  dimensions  are  very  insignifi- 
cant (cf.  p.  25).  This  may  even  be  the  case  for  the 

1  Quite  recently  experiments  on  the  synthetic  action  of  trypsin  or  pepsin 
seem  to  have  been  followed  by  success.  Taylor  (Univ.  of  Calif.  Publ., 
Pathol.  I,  No.  9,  1907,  p.  343)  synthetised  protamin  from  its  products  of 
decomposition  by  means  of  trypsin,  and  T.  Brailsford  Robertson  (Univ.  of 
Calif.  Publ.,  Pathol.  Ill,  No.  9,  1907,  p.  59)  synthetised  paranuclein  from 
its  products  of  decomposition  by  subjecting  them  to  the  action  of  pepsin. 


VELOCITY  OF  REACTION.   HETEROGENEOUS  SYSTEMS  135 


finely  powdered  coagula  of  egg-white  or  the  emulsified  fat 
drops  in  Volhard's,  Stade's,  and  Engel's  experiments.  But 
with  the  pillars  of  coagula  this  cannot  be  said  to  occur.  In 
this  case  we  must  suppose  that  the  liquefied  part  of  the 
column  is  carried  away  into  the  liquid  about,  so  that  this  is 
able  to  attack  new  portions  of  the  pillar.  Here,  therefore, 
the  reaction  is  going  on  at  the  surface  of  the  coagulated 
substrate,  and  immediately  below  it,  and  the  constancy  of 
the  product  qt  shows  that  under  constant  conditions  the 
number  of  molecules  digested  in  one  second  is  proportional 
to  the  concentration  of  the  ferment  in  the  surrounding 
liquid  (and  to  the  surface,  which  remains  nearly  constant). 
Madsen  and  Walbum  have  investigated  the  progress  of 
dissolution  of  casein  by  means  of  trypsin.  Ten  g.  of  casein 
in  the  form  of  the  powder  were  suspended  in  100  c.c.  of 
a  i  per  cent  solution  of  trypsin  and  held  at  constant  tem- 
perature. In  order  to  prevent  the  casein  from  subsiding, 
the  flask  containing  the  mixture  was  steadily  shaken. 
After  different  time  intervals  samples  were  removed,  and 
the  undissolved  quantity  of  casein  determined  by  means  of 
its  content  of  nitrogen  —  determined  according  to  the 
method  of  Kjeldahl.  The  progress  of  dissolution  is  shown 
by  the  following  table  (temperature,  34.1°)  :  — 


TIME 
(hours) 

NITROGEN 
(obs.) 

NITROGEN 
(calc.) 

TIME 
(hours) 

NITROGEN 
(obs.) 

NITROGEN 
(calc.) 

0 

O.I  I 

O.  II 

48 

O.o6o 

0.058 

o-5 

0.108 

0.109 

72 

0.0486 

0.0464 

2-5 

O.  IO2 

0.105 

101 

0.0374 

0.0376 

6 

O.  IOO 

0.099 

125 

0.0329 

0.0325 

ii 

0.096 

0.091 

1  68 

0.0274 

0.0269 

24 

0.076 

0.076 

192 

0.0236 

0.0236 

33 

0.070 

0.068 

136  LECTURES  ON  IMMUNITY 

The  nitrogen  (calc.)  is  calculated  according  to  the  equa- 
tion for  a  bimolecular  process,  and,  as  will  be  seen,  the 
agreement  is  very  satisfying.  The  relation  which,  after 
Bayliss's  experiment,  is  very  unexpected,  may  be  regarded 
as  a  purely  empirical  one.  The  reaction-constant  is  o.  173. 
It  increases  with  temperature,  as  might  be  expected.  At 
37°  C.  it  reaches  the  value  0.194,  corresponding  to  an  in- 
crease in  the  proportion  1.485  :  i  in  an  interval  of  10°  C. 
O  =7400). 

Many  of  the  most  important  processes  of  normal  life 
occur  in  heterogeneous  systems.  As  is  seen  from  the  fol- 
lowing examples,  they  behave  as  regards  the  velocity  of 
reaction  quite  like  enzymic  processes.  All  of  them  pos- 
sess an  optimum  at  about  4O°-5o°  C.,  and  in  the  vicinity  of 
o°  C.  the  velocity  of  reaction  sinks  rapidly  with  tempera- 
ture. 

The  most  important  of  these  processes  are  the  phenom- 
ena of  assimilation  and  of  respiration  of  carbonic  acid  by 
plants.  As  van't  Hoff1  remarks,  the  observations  of 
Clausen2  seem  to  indicate  that  in  the  interval  of  tempera- 
ture o°-25°  C.  the  quantity  of  carbonic  gas  given  off  by 
seedlings  of  wheat,  lupins,  and  flowers  of  syringa  increases 
with  temperature  in  the  proportion  1 12.5  for  an  increase 
of  10  degrees  (/i=  14,800).  The  three  processes  show  an 
optimum  at  41,38  and  42°  C.  respectively. 

Godlewski3  showed  that  the  assimilation  of  a  leaf  of 
four  different  plants  —  the  most  regular  results  were  those 

1  Van't  Hoff:    Vorlesungen  uber  theoretischc  und physikalische  Chemie,  2d 
ed.,  1.  224  (1901);  E.  Cohen:    Vortrage  f.  Arzte,  p.  43  (1901). 

2  Claussen:  Landwirtsch.  Jahrb.,  19.  892  (1890). 

8  Godlewski :  Arbeiten  des  botanischen  Instituts  in  Wurzburg,  1.  243 
(1872), 


VELOCITY  OF  REACTION.     HETEROGENEOUS  SYSTEMS     137 


of  Typka  latifolia  —  increases  with  the  content  of  carbonic 
acid  in  the  surrounding  air,  and  nearly  proportionally  with 
it,  up  to  about  2  per  cent.  An  optimum  occurs  at  about  6 
per  cent.  At  further  increase  the  assimilation  decreases, 
but  very  slowly.  This  process  was  recently  studied  by 
Miss  Gabrielle  Matthaei,1  who  found  that  the  assimilation 
of  carbonic  acid  by  a  leaf  of  Pnmus  Laurocerasus  increases 
with  temperature  in  the  following  manner  (for  a  leaf  of 
50  cm.2  and  in  one  hour)  :  — 


TEMP. 

ASSIMILATION  MILLIGRAMMES  OF  COz 

obs. 

calc. 

o 

1-75 

i-75 

10 
20 

4.2 
8.9 

3-79 

7.81 

30 

37 

IS-7 
23-8 

15-3 

23-8 

The  process  is  in  all  points  analogous  to  the  action  of 
ferments.  The  chlorophyll  may  here  be  regarded  as  the 
acting  ferment.  The  value  of  /*  is  11,940.  In  these 
figures  we  observe  already  a  greater  increase  at  lower  tem- 
perature than  the  formula  indicates.  If  the  temperature 
falls  below  o°,  the  assimilation  sinks  very  rapidly,  so  that 
at  —6°  C.  the  observed  figure  is  only  0.2  mg.,  correspond- 
ing to  a  value  of  /*  between  o  and  —6°  C.,  about  ten  times 
greater  than  between  o  and  37.  Above  this  latter  tem- 
perature again  the  assimilation  sinks  with  rising  tempera- 
ture until  the  leaf  dies.  This  evidently  depends  on  a  de- 
struction of  the  functions  of  the  chlorophyll  at  very  low  or 
at  higher  temperatures. 

1  Gabrielle  Matthaei :  Phil.  Trans.  Roy.  Soc.,  Ser.  B,  197.  47  (1904).  Cf. 
Kanitz:  Zeitschr.f.  Elektroch.^  No.  42  (1905). 


138  LECTURES  ON  IMMUNITY 

Similar  observations  may  be  made  regarding  the  growth 
of  eggs  of  animals  after  their  fertilisation,  as  observed  by 
Hertwig  and  Karl  Peter.1  The  development  of  these  eggs 
was  followed  by  means  of  observations  of  the  cell-division 
which  went  on  much  more  rapidly  at  higher  than  at  lower 
temperatures.  Even  chemical  influences,  especially  a 
small  addition  of  hydroxyl-ions  to  the  sea  water,  are  often 
very  remarkable.  The  eggs  of  Arbacia  develop  a  little 
more  rapidly  in  sea  water  containing  2  c.c.  of  o.  I  n.  alkali 
in  100  c.c.  of  water  than  if  no  alkali  has  been  added.  An 
equivalent  amount  of  HC1  retards  the  development.2  The 
increase  (/)  for  increase  of  the  temperature  10°  C.  and  the 
corresponding  value  of  ft  are  given  below.  They  are 
valid  for  a  mean  temperature  of  about  16°  C.  :  — 

Eggs  of  Echinus  microtuberculatus  —  First  stage  /=  2. 29  yu,  =  1 3,700 

Later  stages  2.03  11,700 

Eggs  of  Sphtxr  echinus  granularis  First  stage  2.30  13,800 

Later  stages  2.08  12,100 

Eggs  of  Ranafusca  (Hertwig)  First  stage  2.23  13,300 

Later  stages  3.34  20,000 

As  we  see,  ^  is  of  quite  the  same  order  of  magnitude  as 
that  for  the  production  or  assimilation  of  carbonic  acid  by 
green  plants.  Further,  at  low  temperatures  (3-5° C.)  the 
/>&  for  the  eggs  of  the  frog  has  a  very  high  value  —  about 
ten  times  those  given  above ;  and  at  the  temperatures  of 
over  37°  C.  the  life  process  is  hindered  by  increase  of  tem- 
perature. In  a  similar  manner  behaves  the  heart-beat  of 

1  Hertwig:  Archiv  f.  mikrosk.  Anatomic,  51.  319  (1898);  Karl  Peter: 
Archiv  f.  Entwicklungsmechanik,  20.  130  (1905). 

2J.  Loeb:  Archiv  /  Entwicklungsmechanik,  7.  631  (1898).  Cf.  above, 
the  influence  of  alkalies  and  acids  on  the  velocity  of  destruction  of  lysins. 


VELOCITY  OF  REACTION.      HETEROGENEOUS  SYSTEMS     139 

the  Pacific  terrapin  (Clemmys  mamorata),  according  to  ob- 
servations of  Charles  Snyder.  1  His  observations  give  the 
following  values  for  the  number  of  heart-beats  in  one 
minute :  — 

Temp.  o       2.5       5      10      15        20      25       30     35        37.5     40 

Number      0.75     3.2    4.9     7.8     9.7     20.7     27.3     46     48.6    48.2    43.3 
Do.  calc.     2.4       3.2    4.2     7.0  11.4     18.5     29.3     46     71        87.7  106 

/-i  is  found  to  be  16,060.  As  is  seen  from  the  figures,  the 
action  of  the  heart  has  an  optimum.  This  circumstance 
probably  depends  upon  changes  in  the  protoplasms  near 
o°  and  50°  ;  in  the  latter  case  coagulation  occurs.2  There- 
fore the  calculated  values  coincide  with  the  observed  ones 
only  within  a  certain  interval,  2.5-30  degrees.  The  rapid 
increase  in  the  neighbourhood  of  the  freezing  point  is  very 
similar  to  that  found  for  the  two  other  phenomena  of  life 
studied  above. 

Another  process  of  great  practical  importance  caused 
by  living  cells  is  the  production  of  alcohol  and  carbonic 
acid  from  glucose  by  yeast  plants.  This  process  has  been 
investigated  very  thoroughly  by  Aberson.3  He  found  that 
the  formula  of  Henri  is  valid  for  this  reaction,  as  will  be 
seen  from  the  following  figures,  in  which  the  quantity  of 
glucose  (A  —  x)  was  determined  by  means  of  a  polarimeter. 
A  is  the  beginning  concentration,  A  —  ^rthe  corresponding 
quantity  after  /  minutes.  The  temperature  was  for  the 
first  series  17.5°,  for  the  second  27°  C. 


1  Charles  D.  Snyder :  University  of  California  Publications,  Physiology,  2. 
125  (1905). 

2  Loeb  :    Vorlesungen  uber  die  Dynamik  der  Lebenserscheinungen,  p.  155 
(1906). 

8  Aberson:  Rec.  d,  tray.  chim.  /.  Pays-Bas  et  de  la  Belgique,  22.  78  (1903), 


140  LECTURES  ON  IMMUNITY 

PRODUCTION  OF  ALCOHOL  BY  MEANS  OF  YEAST 


t 

A  -  x 

,     io5  ,       A  +  x 
K=TloSA^c 

t 

A-  x 

..     io5  ,       A  +  jf 
*-=Tlog  — 

0 

30-7 

— 

o 

30.5 



43 

29.9 

26.3 

41 

28.3 

76.5 

107 

28.7 

26.5 

86 

25.8 

78.5 

196 

27.1 

26.1 

149 

22.6 

77-3 

269 

25-7 

26.5 

240 

18.2 

77.2 

393 

23-5 

26.4 

300 

I5.8 

76.1 

432 

22.8 

26.5 

357 

13.5 

76.5 

5'2 

21.4 

26.5 

493 

II.7 

77-5 

590 

20.5 

26.3 

5H 

9.6 

76.5 

613 

19.7 

26.5 

529 

8.1 

78.1 

790 

I7.I 

26.2 

752 

4.1 

76.0 

The  mean  values  are  26.85  and  77-  From  these  we  cal- 
culate the  value  of  ^  =  15,607.  By  means  of  this  value 
Aberson  calculated  his  other  experiments,  and  found  an 
excellent  agreement  with  the  observations.  As  illustra- 
tion the  following  figures  may  be  cited  :  — 


TEMP. 

^"obs. 

^calc. 

15-4 

31.2 

31.2 

21.0 

55.6 

524 

27.0 

90.0 

89.2 

32.0 

139.8 

136.8 

In  many  cases  the  quantity  of  yeast  was  augmented  by 
cellular  multiplication  during  the  experiment;  in  such 
cases  a  correction  for  this  circumstance  was  applied.  The 
quantity  of  glucose,  as  well  as  that  of  the  reaction-products, 
had  an  influence  upon  the  constant,  whereby  the  deviation 
of  the  velocity  of  reaction  from  that  valid  for  monomolecu- 
lar  reactions  may  be  explained. 


VELOCITY  OF   REACTION.      HETEROGENEOUS  SYSTEMS     141 

The  production  of  alcohol  and  carbonic  acid  from  glu- 
cose is,  as  Buchner  showed,  not  a  peculiarity  for  the  living 
cell,  as  Pasteur  had  supposed,  but  may  be  performed  by 
dead  yeast-cells  or  an  extract  from  them  called  zymase. 
With  dead  yeast-cells  (Herzog)1  and  with  zymase  (Euler)2 
experiments  have  been  carried  out,  —  in  the  latter  case  the 
reaction  occurs  in  a  homogeneous  medium.  Euler  followed 
the  progress  of  the  reaction  by  measuring  the  quantity  of 
carbonic  acid  developed,  or  with  the  polarimeter  the 
destruction  of  the  sugar.  The  quantity  of  glucose  was 
20  c.c.  of  I  n.  solution.  The  quantity  of  zymase  used 
was  3.6  g.  in  the  first,  1.2  g.  in  the  second  series. 

PRODUCTION  OF  ALCOHOL  FROM  GLUCOSE  BY  MEANS  OF  ZYMASE 


OBSERVATIONS  OF  THE  PRODUCED  QUAN- 
TITY OF  CO3 

OBSERVATIONS  WITH  THE  POLARIMETER 

Time,/(min.) 

A  -  x 

K  10*     A 

Time,*(min.) 

A-x 

.10*      A 

K=TlosA^ 

K  ...  bg-— 

0 

790 

— 

O 

I075 

— 

I98 

709 

2-37 

81 

1018 

2.95 

237 

700 

2.21 

124 

990 

2.90 

323 

672 

2.17 

224 

930 

2.81 

413 

644 

2.15 

324 

877 

2.73 

355 

860 

2.73 

38i 

851 

2.67 

406 

841 

2.63 

730 

700 

2.55 

Here  we  find  a  slow  decrease  in  the  values  of  K  and  not 
an  increase,  in  which  case  the  formula  of  Henri  might  be 
applicable.  It  is  therefore  probable  that  the  agreement 
of  Henri's  formula  with  the  measurements  of  Aberson  is 


1  Herzog:    Hoppe-Seylers  Zeitschr.  37.  149   (1903). 

2  Euler:  Hoppe-Seylers  Zeitschr.  44.  53  (1905). 


142  LECTURES  ON  IMMUNITY 

due  to  some  perturbation  introduced  by  the  life-processes 
of  the  yeast-cells.  Euler,  however,  also  observed  some 
complications  which  require  additional  experimentation 
before  they  can  be  explained.  The  velocity  of  reaction 
increases  more  rapidly  than  the  concentration  of  the  en- 
zyme, and  not  proportionally  to  a  simple  power  of  it.  The 
quantity  decomposed  does  not  increase  with  the  concentra- 
tion of  the  sugar,  but  shows  on  the  contrary  a  relative 
decrease,  if  the  concentration  of  sugar  is  raised. 

The  study  of  the  velocities  of  reactions  in  heterogeneous 
systems  indicates  that  they  behave  very  nearly  in  the  same 
manner  as  in  homogeneous  systems.  This  observation 
has  often  been  made  concerning  the  velocity  of  reactions 
in  heterogeneous  systems.1  It  depends  upon  the  circum- 
stance that  by  means  of  the  experimental  arrangements 
the  diffusion  goes  on  so  rapidly  that  it  does  not  perturb 
the  chemical  processes.  If  capillary  tubes  are  employed, 
this  cannot  be  said  to  be  the  case,  and  therefore  Mett's 
tubes  should  not  be  used  for  quantitative  measurements. 

Even  the  influence  of  temperature  on  these  reactions  is 
of  the  same  order  of  magnitude  as  for  those  processes  in 
which  different  substances  react  with  one  another  in 
homogenenous  systems.  Remarkable  is  the  low  value  for 
the  haemolysis  by  means  of  sodium  oleate  (/4  =  3800).  The 
agglutination  of  erythrocytes  by  means  of  mercuric  chloride 
and  ricin  give  nearly  the  same  values  for  //,  (17,900  and 
17,200)  and  the  values  for  JJL  for  the  two  different  bacterio- 
agglutinins  are  not  of  very  different  order  (>i=  30,100 
for  coli-agglutinin,  p=  37,200  for  typhoid-agglutin).  Near 
this  value  also  stands  that  for  haemolysins  of  bacterial 

1  Cf .  Goldschmidt  :    Zeitschr. / physikal.  CAemig,&l,  235  (1899). 


VELOCITY  OF   REACTION.      HETEROGENEOUS   SYSTEMS     143 

origin  (streptolysin,  //.  =  31,900;  vibriolysin,  /-t  =  27,300 ;  for 
tetanolysin  the  time  of  reaction  has  been  too  long  to  yield 
correct  value  for  /A).  Close  to  these  values  are  the  highest 
ones  of  those  for  the  haemolytic  action  of  acids  and  bases 
(ammonia,  ^  =  27,000;  propionic  acid,  ^  =  25,000).  The 
values  of  p  for  these  substances  have  already  been  dis- 
cussed at  length  above. 

For  comparison  I  tabulate  the  other  values  of  JJL  given  in 
this  chapter :  — 

Digestion  of  powdered  casein  by  means  of  trypsin  ..../*=   7,400 
Saponification  of  emulsion  of  yolk  by  means  of  pancreatic  juice  /*  =  13,600 

Respiration  of  different  plants  (mean  value) p  =  14,800 

Production  of  alcohol  by  means  of  yeast-cell /*  =  15,600 

Assimilation  process  in  plants /A  =  12,000 

Cell-division  in  different  eggs  (mean  value) jx  — 14,100 

Heart-beats  of  the  Pacific  terrapin /A  =  16,060 

The  p  values  are  in  general  of  the  same  order  of  mag- 
nitude as  in  the  case  of  homogeneous  reactions.  The 
great  similarity  of  the  values  of  n  for  the  different  life- 
processes  would  scarcely  seem  to  be  accidental. 


COLLEGE    OF    DENTISTRY 
UNIVERSITY  OF  CALIFORNIA 


COLLEGE    OF    DENTISTRY 

UNIVERSITY  OF  CALIFORNIA 

CHAPTER  V 

EQUILIBRIA   IN   ABSORPTION   PROCESSES 

THE  most  simple  of  all  processes  belonging  to  this 
domain  seems  to  be  the  absorption  of  agglutinin  by  the 
corresponding  bacteria.  If  we  add  an  agglutinin  to  a  sus- 
pension of  bacteria  (whether  living  or  dead  makes  little 
difference),  the  bacteria  clump  together  and  fall  to  the 
bottom  of  the  container.  If  after  the  sedimentation  of  the 
bacteria,  we  decant  the  supernatant  fluid  and  again  deter- 
mine its  agglutinating  power,  we  find  that  it  has  decreased 
in  large  measure.  We  conclude,  therefore,  that  a  large 
fraction  of  the  agglutinin  has  been  absorbed  by  the  bac- 
teria. Eisenberg  and  Volk  have  studied  this  phenomenon 
on  a  rather  large  scale.  The  two  following  tables  give 
their  results  with  the  serum  of  a  horse  that  had  been  in- 
jected with  typhoid  bacilli,  and  that  of  another  horse  that 
had  been  injected  with  cholera  vibrions.  Different  con- 
centrations of  these  agglutinin-holding  sera  —  prepared  by 
dilution  with  physiological  sodium  chloride  solution  —  were 
brought  in  contact  with  the  same  quantities  of  suspensions 
of  typhoid  bacilli  or  of  cholera  vibrios.  The  quantity  of 
agglutinin  added  is  given  in  the  column  headed  T,  the 
quantity  of  agglutinin  absorbed  by  the  bacteria  is  found 
under  C\  the  quantity  remaining  in  the  liquid  is  called 
.#ob8.  Evidently  BQ^  -f-  C=T.  In  the  next  column  is 
tabulated  the  figures  for  J3c&}c.t  calculated  in  a  manner  to  be 
indicated  below. 

144 


EQUILIBRIA  IN  ABSORPTION  PROCESSES  145 

ABSORPTION  OF  TYPHUS  AGGLUTININ  BY  TYPHOID  BACILLI 


r 

C 

*ob, 

^calc. 

K 

2 

2 

o 

O.O2 

— 

2O 

20 

o 

O.y 

— 

40 

40 

0 

2.1 

— 

200 

1  80 

20 

19.7 

24.4 

400 

340 

60 

52.9 

22.6 

Mean 

2,000 
10,000 

1,500 
6,500 

500 

3>5°o 

478 
3,890 

23.7 
28.2 

24.7 

20,000 

11,000 

9,000 

9,  1  60 

25-4 

ABSORPTION  OF  CHOLERA  AGGLUTININ  BY  CHOLERA  VIBRIOS 


T 

C 

*obs. 

^calc. 

K 

2 

2 

0 

0.03 

— 

20 

2O 

O 

I.O 

— 

40 

38 

2 

2.8 

24  1 

67 

60 

7 

6 

16.4 

200 

120 

80? 

27 

(6.5?) 

Mean 

2,000 

1,300 

700 

620 

I6.5 

19 

11,000 

6,500 

4,5°° 

5,260 

23-9 

2O,OOO 

IO,OOO 

10,000 

10,750 

21-5  J 

As  is  evident  from  these  figures,  on  the  addition  of  a 
small  quantity  of  agglutinin  it  is  absorbed  (nearly)  totally ; 
Bobs  is  found  to  =  o.  Indeed,  the  method  of  observation 
does  not  permit  the  observation  of  values  of  B  below 
B  —  i.  On  the  further  addition  of  agglutin  the  absorbed 
fraction  decreases  continuously  until  at  the  end  the  absorbed 
fraction  is  not  greater  than  the  non-absorbed  fraction. 
It  has  been  hitherto  often  assumed  that  the  agglutinin 
was  chemically  bound  in  the  bacteria.  To  carry  out  this 
idea  consequentially,  we  must  suppose  that  the  resulting 


146  LECTURES  ON  IMMUNITY 

compound  is  a  highly  dissociable  one.  For  otherwise  the 
oft-observed  washing  out  of  the  agglutinin  from  this  com- 
pound in  the  bacterium  would  be  inexplicable.  And,  fur- 
thermore, the  absorption  of  the  agglutinin  ought  to  be 
total  until  saturation  was  obtained,  and  thereafter  only  a 
very  slight  increase  (due  to  the  physical  absorption)  ought 
to  be  observed. 

But  even  if  we  suppose  the  compound  to  be  dissociable 
to  a  high  degree,  we  might  expect  that  the  bound  fraction 
of  agglutinin  (C)  should  increase  to  a  limit  value  with  in- 
creasing concentration  of  B  (and  T).  As  Eisenberg  and 
Volk  remark,  no  such  limit  can  be  observed  in  the  results 
of  their  experiments.  Even  the  assumption  that  the 
agglutinin  contains  many  different  kinds  of  "  agglutinin  "  of 
different  combining  powers  does  not  extricate  us  from 
this  difficulty. 

In  favour  of  the  hypothesis  that  the  agglutination  is  the 
consequence  of  a  chemical  combination,  Joos  has  adduced 
some  experiments  on  the  effect  of  partial  additions  of 
agglutinin  to  a  suspension  of  typhoid  bacilli.  He  deter- 
mined the  least  dosage  of  agglutinin  that  is  able  to  agglu- 
tinate all  the  bacteria  in  the  test.  Then  he  added  a  part 
of  this  quantity  to  a  similar  suspension ;  the  agglutination 
was  incomplete.  He  centrifugated  the  solution  and  in  this 
way  segregated  the  agglutinised  bacteria  and  removed 
them.  Then  he  added  a  new  portion  of  agglutinin  to  the 
solution,  and  so  forth,  until  all  the  bacteria  had  been  agglu- 
tinated. The  total  quantity  of  agglutinin  added  in  the 
several  fractions  in  this  manner  was  found  to  be  equal  to 
the  quantity  necessary  to  agglutinate  all  the  bacteria  when 
added  at  once.  Considering  the  great  experimental  errors 


EQUILIBRIA  IN   ABSORPTION   PROCESSES  147 

in  such  observations,  the  conclusion  does  not  seem  to  pos- 
sess a  very  high  degree  of  accuracy.  And  even  if  this 
were  the  case,  it  is  very  probable  that  the  quantities  of 
bacteria  separated  out  in  the  first  fractions  were  rather 
small,  and  under  such  circumstances  it  was  evidently  to 
have  been  expected  that  the  total  quantity  of  agglutinin 
in  the  two  experiments  would  be  nearly  the  same. 

Now  in  regard  to  the  figures  of  Eisenberg  and  Volk,  it 
is  evident  that  a  relation  exists  between  the  absorbed  quan- 
tity of  agglutinin  C  and  the  free  quantity  B.  This  rela- 
tion may  be  expressed  in  a  very  simple  mathematical 
formula,  namely:  — 


With  the  aid  of  this  equation  the  calculated  figures  ^calc. 
are  found.  They  agree  very  well  with  the  observations, 
within  the  errors  of  observation,  as  Dr.  Eisenberg  also  has 
stated.  The  only  observation  in  the  second  series  which 
gives  an  unsatisfactory  agreement  between  the  observed 
and  calculated  values  is  where  ^Ob8.  =  80  and  Bc&lCf  =  27. 
Eisenberg  and  Volk  themselves  state  in  their  original 
memoir  that  this  observation  must  be  influenced  by  some 
occasional  error. 

The  physical  interpretation  of  the  above  formula  is  very 
simple.  It  states  that  the  agglutinin  molecules  are  divided 
between  two  solvents,  the  bacterial  cells  and  the  sur- 
rounding medium,  and  that  of  two  molecules  of  the  free 
agglutinin  are  formed  three  molecules  of  the  absorbed 
agglutinin. 

In  the  experiments  of  Ransom  cholesterin  is  a  sol- 
vent for  saponin,  and  the  existence  of  cholesterin  in  the 
red  blood-corpuscles  causes  the  entrance  of  the  haemo- 


148  LECTURES  ON  IMMUNITY 

lytic  substance  saponin  into  them,  following  which  the  red 
blood-corpuscles  are  poisoned,  so  that  they  give  up  their 
colouring  matter,  the  haemoglobin.  Now  in  a  similar  man- 
ner the  bacterial  cells  contain  some  substance  that  is  a 
good  solvent  for  the  corresponding  agglutinin,  which  is 
thereby  caused  to  enter  the  bacteria  to  a  preponderating 
extent.  The  molecular  weight  of  the  agglutinin  in  the 
bacterial  solvent  is  only  two-thirds  of  the  molecular  weight 
of  the  agglutinin  in  the  surrounding  fluid,  the  physiologi- 
cal salt  solution. 

This  behaviour  of  the  agglutinin  molecules  in  two  sol- 
vents recalls  vividly  the  behaviour  of  benzoic  acid  in  two 
different  solvents,  water  and  benzene.  According  to 
determinations  of  the  freezing  point  of  solutions  of  ben- 
zoic acid,  this  has  in  aqueous  solution  the  molecular  weight 
122,  corresponding  to  the  formula  C6H6COOH;  but  in 
benzene  its  molecular  weight  is  double  that.  Therefore,  if 
we  dissolve  benzoic  acid  in  water,  and  shake  this  solution 
with  benzene,  the  concentration  of  the  aqueous  solution  Ca 
is  related  to  the  concentration  of  the  benzene  solution  Cb 
as  indicated  in  the  following  formula  :  — 


where  K  is  a  constant  factor.  Nernst  verified  this  equa- 
tion by  experiments  on  the  distribution  of  benzoic  acid 
between  water  and  benzene. 

The  great  velocity  of  absorption  is  in  good  agreement 
with  our  interpretation  as  stated  above. 

A  difficult  thing  to  explain  is  the  specificity  of  the  ag- 
glutinins.  The  agglutinin  produced  by  injecting  typhoid 
bacilli  into  the  blood  of  an  animal  is  only  absorbed  by 


EQUILIBRIA  IN  ABSORPTION  PROCESSES  149 

typhoid  bacilli  and  not  by  other  bacteria,  for  instance  not 
by  cholera  vibrios,  and  vice  versa.  Probably  the  cell-- 
membranes of  typhoid  bacilli  are  only  permeable  to  typhoid 
agglutinins,  but  not  to  other  agglutinins.  Normal  sera  con- 
tain different  agglutinins  against  bacteria  and  red  blood- 
corpuscles;  by  shaking  them  with  the  corresponding  bacilli 
or  cells,  it  is  possible  to  separate  the  different  agglutinins. 
Thus  Malkoff  mixed  goat-serum,  that  agglutinates  red 
blood-corpuscles  from  man,  rabbits,  and  pigeons,  with  red 
blood-corpuscles  from  rabbits.  The  centrifugalised  serum 
had  lost  its  agglutinating  power  for  rabbit's  erythrocytes, 
but  not  for  the  two  other  varieties.1 

The  agglutinins  lose  their  agglutinating  power  spon- 
taneously, but  much  more  rapidly  at  high  than  at  low 
temperatures  (cf.  pp.  87  and  91).  Treatment  with  different 
chemical  agents,  as  hydrochloric  and  other  acids,  bases, 
formol,  and  urea,  weakens  them.  The  details  of  these 
circumstances  have  not  been  closely  investigated. 

Just  as  agglutinins  are  absorbed  by  bacteria  and  red 
blood-corpuscles,  so  in  the  same  manner  other  different 
substances  are  absorbed  by  these  cells,  and  probably 
analogous  regularities  are  manifested  in  these  cases. 
Thus  tetanolysin,  ricin,  and  the  different  immune  bodies 
are  absorbed  by  red  blood-corpuscles ;  and  it  seems  to  be 
a  general  law  that  only  such  substances  as  are  absorbed 
by  these  cells  exert  an  influence  upon  them.  Whether  the 
cells  are  living  or  dead,  seems,  as  we  observed  regarding 
the  absorption  of  agglutinins,  to  be  quite  immaterial  if 
the  killing  of  the  cells  has  been  cautiously  accomplished, 
so  that  no  notable  chemical  changes  have  occurred. 

1  Malkoff :  Deutsche  med.  Wochenschrifi,  1900. 


ISO 


LECTURES  ON  IMMUNITY 


Morgenroth  and  I  examined  the  absorption  of  an  im- 
mune-body, prepared  by  the  injection  of  red  corpuscles 
of  ox-blood  into  the  veins  of  a  rabbit.  Another  series  of 
Morgenroth's  experiments  was  carried  out  with  inactivated 
(heated)  serum  from  a  goat  injected  with  sheep's  erythro- 
cytes.  Different  solutions  of  the  immune-bodies  —  their 
strengths  in  an  arbitrary  unit  are  tabulated  under  T- 
were  treated  with  a  constant  quantity  of  erythrocytes  from 
ox  or  sheep  for  about  one  hour  at  low  temperature  and 
then  centrifugalised.  The  centrifugated  liquid  was  exam- 
ined for  its  concentration,  B,  of  immune-body,  by  the 
addition  of  normal  serum  of  the  guinea-pig,  and  measur- 
ing the  haemolytic  power  of  the  haemolysin  produced. 
The  difference,  C,  was  absorbed  by  the  red  blood-cor- 
puscles. Beside  the  observed  figures,  -#ob8.,  for  the  quan- 
tity of  free  immune-body,  are  written  figures  for  -#caic.> 
calculated  by  the  aid  of  the  same  formula  as  that  found  to 
be  valid  for  agglutinins.  The  constants,  K,  of  the  formulae 
were  calculated  to  be  18.3  and  39.5  respectively. 

ABSORPTION  OF  IMMUNE-BODIES  BY  RED  BLOOD-CORPUSCLES 


SERUM  FROM  A  RABBIT  INJECTED  WITH 

SERUM  FROM  A  GOAT  INJECTED  WITH  ERY- 

BOVINE ERYTHROCYTES 

THROCYTES  FROM  SHEEP 

T 

c 

-5ob8. 

-^calc. 

T 

c 

^obs. 

•^calc. 

250 

226 

24 

39 

200 

189.5 

10.5 

10.5 

330 

275 

55 

57 

400 

374 

26 

28.8 

670 

500 

170 

151 

800 

723 

77 

78.4 

i,330 

850 

480 

376 

1,600 

1,384 

216 

211 

2,700 

1,710 

990 

942 

3,200 

2,400 

800 

55° 

5,000 

3.070 

i,93o 

2,050 

6,400 

5,230 

1,170 

1,420 

10,000 

5,800 

4,200 

4,800 

12,800 

9,420 

3,38o 

3,570 

16,700 

7,820 

8,880 

8,870 

33,000 

13,900 

19,100 

19,700 

EQUILIBRIA  IN  ABSORPTION  PROCESSES  151 

As  will  be  seen  from  the  figures,  the  agreement  between 
the  observed  and  the  calculated  figures  is  just  as  good  as 
for  the  agglutinins,  and  wholly  within  the  possible  errors 
of  observation.  The  same  physical  explanation  evidently 
holds  good  for  both  phenomena. 

In  some  recent  investigations  bearing  upon  the  absorp- 
tion of  coli-agglutinin  in  the  bodies  of  the  Bacillus  colt  com- 
munis,  Dreyer  has  found  that  not  only  the  constant  K, 
but  also  the  exponent  n  in  the  equation  C=  KB*  may  turn 
out  different  in  different  experiments,  n  always  falls  near 
unity,  sometimes  it  exceeds  it,  e.g.  in  one  case  n  was  found 
to  be  1.25.  A  closer  investigation  regarding  the  cause  of 
this  variability  seems  very  desirable. 

This  case  has  a  certain  theoretical  significance.  Quite 
recently  the  opinion  has  often  been  ventured  that  the  ab- 
sorption of  agglutinin  by  bacteria  might  be  analogous  to 
the  so-called  adsorption  of  dissolved  substances  by  char- 
coal, or  of  colouring  matter  by  organic  tissues.  Bordet  was 
the  first  to  make  this  assumption,  which  has  recently  been 
upheld  by  Wilh.  Biltz.  Biltz  now  states  that  in  the  theo- 
retically hitherto  little  elucidated  adsorption-process  n  is 
always  lower  than  i ;  for  absorption  by  charcoal  it  is  0.25, 
according  to  Schmidt.  If  therefore  n  is  sometimes  found 
to  exceed  i,  as  in  Dreyer's  work,  we  have  to  abandon  the 
adsorption  hypothesis.  Biltz,  Much,  and  Siebert  for  two 
hours  shook  typhoid  agglutinin  with  the  following  colloidal 
bodies :  silicic  acid  or  hydroxids  of  iron,  zircon,  and  tho- 
rium. It  was  found  that  silicic  acid  had  a  noticeable  and 
the  three  other  substances  a  much  greater  destructive  action 
on  the  agglutinin.  This  seems  to  indicate  that  we  have 
here  to  deal  with  a  real  chemical  influence,  which  is  not 


152  LECTURES  ON  IMMUNITY 

astonishing,  as  many  different  substances  destroy  agglu- 
tinins.  For  absorption  it  is,  on  the  contrary,  generally 
possible  to  show  that  the  absorbed  bodies  (e.g.  dyes)  exist 
on  or  in  the  absorbing  substance,  from  which  they  may 
often  be  washed  out.  The  authors  have  tried  in  vain  to 
poison  animals  by  the  injection  of  hydroxid  of  iron  which 
had  been  shaken  with  diphtheria  poison  or  tetanospasmin, 
which,  just  as  agglutinins,  are  attenuated  by  such  shaking. 
If  these  poisons  had  been  absorbed  like  agglutinins  by  the 
bacteria,  i.e.  in  a  reversible  way,  then  a  strong  poisonous 
effect  should  have  manifested  itself  in  the  injected  animals. 
But  not  a  trace  of  the  expected  effect  was  observed.  Biltz, 
Much,  and  Siebert  were  then  led  to  the  conclusion  that 
the  hypothesis  of  absorption  is  not  tenable. 

They  have  therefore  taken  up  an  idea  incidentally  sug- 
gested by  Nernst  for  the  explanation  of  the  neutralisation 
of  toxins  by  their  antibodies.  This  idea  is  not  very  differ- 
ent from  that  of  Behring.  (Cf.  p.  29.)  Let  us  suppose 
we  have  finely  divided  colloidal  platinum  (Bredig's  "an- 
organic ferment")  and  hydrogen  peroxid.  The  peroxid 
condenses  upon  the  fine  metal  particles  and  thereafter  it  is 
decomposed.  This  would  correspond  to  the  condensation 
of  a  toxin,  e.g.  ricin,  on  the  colloidal  particles  of  its  anti- 
body, antiricin,  and  its  subsequent  decomposition.  The 
antiricin  itself  should  be  slowly  attacked  by  the  ricin, 
just  as  the  platinum,  if  it  were  oxidisable  by  the  hydrogen 
peroxid.  This  explanation  is  incompatible  with  the  fact 
that  the  ricin  can  be  recovered  after  it  is  "neutralised," 
therefore  the  neutralisation  cannot  depend  upon  its  de- 
struction. It  seems  that  the  advocates  and  adherents  of 
this  idea  (the  schools  of  Nernst  and  of  Ehrlich)  had  an 


EQUILIBRIA  IN  ABSORPTION   PROCESSES  153 

intuition  that  it  would  conflict  with  experience.  Evidently 
it  agrees  with  the  experiments  in  the  shaking  of  poisons 
with  colloidal  hydroxids  (except  in  that  these  substances 
are  not  chemically  attacked  by  the  poisons),  but  it  does  not 
harmonise  with  our  experience  with  the  reactions  of  bac- 
teria to  their  agglutinins. 

It  may  also  be  emphasised  that  the  solutions  of  anti- 
toxins do  not  behave  as  suspensions,  as  is  seen  in  their 
diffusibility  in  jelly,  which  is  not  observed  with  suspended 
particles. 

There  is  another  phenomenon  which  we  encounter  in 
the  use  of  some  kinds  of  agglutinins,  e.g.  such  as  have 
been  weakened  by  acids,  or  other  chemicals,  or  by  heat. 
These  modified  agglutinins  display  an  increase  in  their 
agglutinating  power  until  a  maximum  of  agglutination  is 
reached.  Thereafter  new  additions  of  agglutinin  dimin- 
ish the  effect  and  at  a  high  concentration  of  the  agglu- 
tinin the  agglutination  ceases.  A  similar  behaviour  is 
characteristic  of  many  salts.  Without  the  presence  of 
some  salts  in  the  solution,  no  agglutination  takes  place,  and 
the  same  is  also  true  for  very  high  concentrations  of  the 
salts.  With  increasing  concentration  of  the  salt  (above  the 
optimum  value)  a  greater  quantity  of  agglutinin  is  neces- 
sary to  produce  agglutination,  and  at  a  concentration  of  the 
salt  above  a  certain  limit  value  the  agglutination  fails. 
On  small  additions  of  salts  the  agglutinated  quantity 
seems  to  be  proportional  to  the  added  quantity,  which 
might  be  expected  on  the  basis  of  most  of  the  hypotheses 
regarding  the  nature  of  agglutination,  and  not  only  from 
the  chemical  one,  as  Joos  supposes. 

In  the  theory   of  immunity  we  find   many  analogous 


154  LECTURES  ON  IMMUNITY 

cases  where  maxima  or  minima  of  a  certain  effect  are 
observed  at  a  certain  concentration  of  the  reacting  sub- 
stance. One  of  the  most  startling  of  these  phenomena  is 
observed  on  injection  of  a  mixture  of  the  botulismus-poison 
produced  by  Bacillus  botulinus,  and  its  antibody,  obtained 
from  the  blood-serum  of  animals  that  have  been  injected 
with  this  poison.  Madsen  used,  for  instance,  a  mixture  of 
o.i  c.c.  with  0.0013  c.c.  of  its  antitoxin.  The  injection  of 
ten  such  doses  in  a  guinea-pig  (of  250  g.  weight)  had 
no  effect;  two  doses  gave  just  a  trace  of  illness  charac- 
terised by  a  peculiar  flaccidity  of  the  animal;  one  dose 
caused  a  flaccidity  lasting  four  to  seven  days.  Injections 
of  between  0.013  and  0.5  doses  had  a  lethal  effect,  and  the 
maximal  toxicity  was  shown  by  a  o.i  dose,  the  animal  dying 
after  only  two  days ;  o.oi  dose  was  no  longer  lethal,  but 
caused  flaccidity  lasting  seven  days ;  and  0.003  dose  only  a 
trace  of  flaccidity  lasting  only  one  day. 

Another  similar  instance  with  a  minimum  and  a  maxi- 
mum of  effect  is  shown  in  haemolysis  by  means  of  sapo- 
nin  (Madsen  and  Walbum),  an  extract  from  the  roots  of 
Saponaria;  8  c.c.  of  a  suspension  of  I  per  cent  of  erythro- 
cytes  from  horse  blood  was  added  to  the  following  quanti- 
ties of  a  0.02  per  cent  solution  of  saponin  with  water  up  to 
a  total  quantity  of  10  c.c.  This  mixture  was  placed  for  three 
hours  at  37  °  C.  and  thereafter  cooled  on  ice  and  the  de- 
gree of  haemolysis  in  per  cent  measured  on  the  following 
day  after  the  unattached  erythrocytes  had  subsided. 

Quantity  of  saponin  in  c.c.  =    I     0.7     0.5     0.4     0.3     0.25     0.2     0.17     O 
Haemolysis  in  per  cent  =          35    16      18      30     36       36       45       41      o 

Similar  observations  were  also  made  with  mixtures  of  sa- 


EQUILIBRIA  IN  ABSORPTION   PROCESSES  155 

ponin  and  cholesterin,  which  acts  as  an  antitoxin  against 
saponin. 

Even  tetanolysin  sometimes  gives  such  maxima  of  effect 
for  a  certain  concentration,  if  the  time  of  action  is  rela- 
tively short.  After  a  prolonged  action  the  maximum  dis- 
appears. This  maximum  seems  therefore  to  be  related  to 
the  velocity  of  the  reaction  and  not  to  the  final  equilibrium. 
Probably  the  same  would  occur  also  with  the  saponin  if 
its  action  could  be  prolonged  for  a  sufficient  time. 

Reactions  of  this  kind  are  often  explained  as  due  to  the 
presence  in  the  mixture  of  two  substances  of  inverse  effect. 
Thus  it  is  supposed  that  agglutinin  treated  with  acids,  etc., 
contains,  besides  the  real  agglutinin,  a  substance  called 
agglutinoid,  which  hinders  the  agglutination.  At  higher 
concentrations  the  bacilli  are  supposed  to  absorb  chiefly 
the  agglutinoid  and  not  the  agglutinin  ;  at  lower  concen- 
trations both  are  supposed  to  be  absorbed.  This  explica- 
tion seems  to  me  to  have  no  advantage,  to  mean  no  more 
than  the  relation  of  the  simple  fact  itself,  besides  being 
much  more  difficult  to  remember.  Furthermore,  it  seems 
more  simple  to  suppose  that  the  reacting  substance  exerts 
two  different  actions  on  the  cells,  of  which  the  one,  appear- 
ing at  higher  concentrations,  hinders  the  other,  prevailing 
at  lower  concentrations.  Such  a  behaviour  is  not  rare  in 
common  chemistry.  Thus,  for  instance,  the  addition  of 
alkali  to  a  solution  of  aluminium  chloride  gives  a  precipi- 
tate of  aluminium  hydrate,  which  is  dissolved  on  further 
addition  of  alkali. 

In  a  brochure  dealing  with  the  properties  of  colloids  Biltz1 

1Biltz:  Gottinger  Nachrichten,  math.-phys.  Klasse  1904,  I,  Zeitschr.  f. 
ph.  Ch.  48.  615  (1904). 


156  LECTURES  ON  IMMUNITY 

recalls  attention  to  the  oft-observed  fact  that  in  gen- 
eral positive  colloids  (which  wander  in  the  electric  field  in 
the  same  manner  as  cations)  precipitate  negative  colloids 
(which  wander  in  the  same  direction  as  anions  under  the 
influence  of  the  electric  current).  This  reminds  one  some- 
what of  the  specificity  of  agglutinins.  As  we  shall  see 
later  on,  Henri  accepted  this  idea,  but  later  he  found  it  dis- 
proved by  experiments  on  agglutinins.  Biltz  found,  further, 
that  in  the  precipitation  of  colloids  optima  are  found. 
Thus,  for  instance,  the  addition  of  1.62  mg.  oxid  of  zir- 
con gave  a  more  abundant  precipitate  with  1.4  mg.  gold 
in  colloidal  solution  than  greater  or  less  quantities;  3.25 
mg.  ZrO2  gave  no  precipitate  at  all.  In  the  same  man- 
ner behaved  4  mg.  thorium  oxid  (as  colloidal  hydrate) 
with  a  colloidal  solution  containing  5.5  mg.  SO2S3. 

In  this  point  also  the  colloids  present  analogies  with 
common  dissolved  inorganic  substances. 

Analogous  effects  are  observed  as  especially  character- 
istic of  precipitins,  and  we  will  return  to  this  special 
question  when  we  later  consider  them. 

Regarding  the  influence  of  salts  upon  agglutination,  we 
possess  a  thorough  investigation  of  Bechhold.  He  used 
typhoid  bacilli,  which  were  cultivated  in  bouillon  and 
thereafter  killed  with  formalin  and  washed  by  repeated 
suspension  in  distilled  water,  and  followed  by  subsequent 
centrifugation.  These  bacteria  were  in  some  experiments 
used  in  their  natural  state.  One  c.c.  of  a  suspension  was 
mixed  together  in  a  test-tube  with  i  c.c.  of  the  salt  solu- 
tion under  investigation.  The  test-tube  was  placed  for 
24  hours  in  an  incubator  at  37°  C.  and  its  content  then 
examined.  The  degree  of  agglutination  was  tested  by 


EQUILIBRIA  IN  ABSORPTION   PROCESSES  157 

looking  through  the  tube  against  a  printed  paper  and 
expressed  corresponding  to  one  of  the  four  following 
degrees :  Liquid  completely  clear,  perfect  agglutination ; 
Most  bacteria  subsided,  but  liquid  not  wholly  clear,  strong 
agglutination;  Some  bacteria  subsided  and  agglomerated, 
no  clearing  of  the  liquid,  weak  agglutination;  No  appre- 
ciable change  of  the  liquid,  no  agglutination. 

In  other  experiments  the  bacteria  used  had  been  treated 
with  serum  containing  agglutinin,  nitrate  of  lead,  ferric-sul- 
phate, alcohol,  acids,  or  uranium  acetate  (which  all  agglu- 
tinate them),  and  thereafter  thoroughly  washed  until  the 
wash-water  did  not  show  any  reaction  of  the  agglutinating 
substances.  The  bacteria  treated  in  these  different  man- 
ners may  be  called  sero,  lead,  iron,  alcohol,  acid,  and 
uranyl  bacilli  respectively.  The  bacteria  had  then  been 
altered  so  that  they  behaved  in  a  different  way  to  salt- 
solutions  than  did  the  original  bacteria.  On  the  addition 
of  sulphuretted  hydrogen  to  the  bacteria  treated  with  lead, 
these  were  coloured  black,  which  proves  that  the  bacteria 
had  retained  the  lead  in  spite  of  the  washing.  For  a  com- 
parison Bechhold1  examined  the  behaviour  of  suspensions 
of  mastic,  prepared  by  adding  some  drops  of  an  alcoholic 
solution  of  this  material  to  water  (so-called  "a  mastic"), 
or  some  drops  of  water  to  the  alcoholic  solution  (" (3  mas- 
tic ").  The  experiments  on  the  agglutination  of  this  last 
emulsion  were  done  at  ordinary  room  temperature,  as  the 
suspended  matter  would  dissolve  at  37°. 

In  the  first  place  an  influence  of  the  time  of  reaction 
was  noted.  Suspensions  of  sero-bacilli  mixed  with  0.05, 
0.025,  or  0.012  normal  solutions  of  sodium  chloride  or 

1  Bechhold:  Zdtschr . f. ph.  ^.,48.385  (1904). 


iS8 


LECTURES   ON   IMMUNITY 


sodium  iodide  were  completely  agglutinated  in  50,  90,  and 
1 20  minutes  respectively;  normal  bacilli  are  not  agglu- 
tinated at  all  by  these  solutions.  On  the  other  hand, 
sero-bacilli  are  less  affected  than  normal  bacilli  by  some 
solutions,  for  instance  0.0033  n.  silver  nitrate  or  0.005  n- 
hydrochloric  acid.  After  a  time  of  15,  50,  and  1440 
minutes  these  preparations  gave  the  following  results:  — 


NORMAL  BACILLI 

SERO-BACILLI 

Treatm.  with  0.0033  n.  AgNO3 
Treatm.  with  0.005  n-  *IC1 

15' 
weak 
weak 

5°' 
perf. 
perf 

1440' 
perf. 
perf. 

15' 
no 
no 

so' 
weak 
weak 

1440' 
perf. 
perf. 

Agglutina- 
tion 

These  and  other  similar  experiments  indicate  that  the 
agglutination  requires  time  (cf.  p.  116).  Further,  a  certain 
concentration  (limit-value)  of  the  salt-solution  is  necessary 
to  give  an  appreciable  agglutination.  The  following  table 
gives  the  limit  value  in  o.ooi  n.  of  the  concentration  for 
different  salts.  The  sign  co  indicates  that  even  the 
strongest  salt-solutions  did  not  agglutinate.  The  quanti- 
ties of  salt  necessary  for  the  first  trace  of  agglutination 
have  the  greatest  value  for  a-mastic,  then  come  /3-mastic 
and  normal  bacilli,  and  after  them  sero-bacilli,  which  are 
the  most  sensitive  to  salts.  The  salts  of  alkalies,  alkaline 
earths,  and  magnesia  exert  little  or  no  influence  on  common 
bacteria.  The  agglutinating  power  is  greater  for  salts  of 
trivalent  metals  than  for  those  of  divalent  metals.  A 
very  strong  influence  is  exerted  by  the  acids,  especially 
the  strong  ones.  The  anions  seem  to  exert  very  little 
influence. 


EQUILIBRIA  IN  ABSORPTION   PROCESSES 


159 


PREPARA- 
TION 

a 

MASTIC 

ft 

MASTIC 

NOR- 
MAL 

BACILLI 

SERO- 

BACILLI 

PREPARA- 
TION 

a 
MAS- 
TIC 

ft 

MAS- 
TIC 

NOR-I 

MAL 

BAC- 
ILLI 

SERO- 

BAC- 
ILLI 

KOH 

00 



00 

00 

MgS04 

IOO 



00 

2-5 

bad 

1000 

10 

00 

25 

Mg(N03)2 

100 



— 

— 

Nal 

— 

— 



25 

CaCl2 

5° 

— 

00 

4-5 

NaNOs 

— 

— 



25 

CaN206 

50 



— 

— 

Na2SO4 

— 

50 

— 

50 

BaO2H2 

5° 

— 

25 

25 

Pbl 

— 

— 



25 

BaCl2 

5° 

5 

oo 

5 

HgN03 

1.25 

— 

I 

°-5 

BaN206 

5° 

— 

— 

— 

AgNO3 

I25 

— 

25 

I 

ZnS04 

IOO 

— 

10 

I 

ZnN2O6 

50 

— 

— 

— 

HC1 

10 

1.25 

I 

°-5 

CdS04 

25 

— 

10 

I 

H2S04 

10 

— 

I 

0.25 

CoN2O6 

50 

— 

— 

2.5 

CH3C02H 

500 

— 

I 

i 

NiN206 

5° 

— 

— 

2.5 

o-Amidoben 
zoic  acid 

— 

— 

5 

5 

Ni(C2H302)2 

25 

— 

25 

2.5 

A12(S04> 

o-5 

— 

0.25 

0.25 

PbN206 

5 

— 

2.5 

O.I 

A1(N03)8 

°-5 

— 

— 

— 

CuCl2 

10 

— 

2.5 

I 

Fe2(S04)3 

°-5 

— 

0-5 

O.I 

CuSO4 

10 

— 

2.5 

— 

Fe  (N03)3 

i 

— 

— 

— 

CuN2O6 

5 

— 

— 

o-5 

FeCl3 

i 

— 

— 

— 

Cu(C2H302)2 

5 

2-5 

— 

— 

PtCl4 

10 

— 

2-5 

o-5 

HgCl2 

00 

— 

2.5 

o-5 

The  salts  of  (univalent)  mercury  and  silver  differ  rather 
widely  from  those  of  other  univalent  ions.  Probably  they 
form  nearly  insoluble  chemical  compounds  with  the 
albuminous  matter. 

In  other  experiments  Bechhold  investigated  the  retard- 
ing influence  of  small  additions  of  gelatin,  serum,  gum 
arabic,  extract  of  typhoid  bacilli  or  of  leeches  on  mastic 
emulsion.  Gelatin  did  not  exert  such  an  influence  on 
normal  bacilli,  sero-bacilli,  or  lead  bacilli.  The  alcohol, 
acid,  or  uranyl  bacilli  display  properties  lying  between 
those  of  normal  bacilli  and  of  sero-bacilli,  but  their  aggluti- 
nation was  lowered  by  the  addition  of  gelatin.  Probably 
the  addition  of  gelatin  or  serum  covers  the  suspended  par- 


160  LECTURES  ON   IMMUNITY 

tides  of  mastic  with  a  thin  film,  after  which  the  particles 
behave  as  if  they  consisted  of  drops  of  gelatin  or  serum. 

Recently  there  have  been  many  efforts  made  to  place  in 
parallel  the  properties  of  egg-white  and  its  derivatives,  as 
peptons  or  albumoses,  with  those  of  inorganic  colloids, 
which  after  all  consist  of  suspensions  of  particles  of  ultra- 
microscopic  magnitude.  These  are  generally  precipitated 
by  the  solution  of  very  small  quantities  of  salts  in  the 
suspending  water,  and  they  assume  an  electric  charge 
on  contact  with  the  water,  whereby  they  wander  to  the 
one  or  to  the  other  pole  of  a  battery  submerged  in  the  solu- 
tion. The  solutions  of  egg-white  and  its  derivatives  seemed 
at  first  to  behave  in  the  same  manner.  But  as  Bechhold 
says,  the  albumoses,  etc.",  do  not  behave  otherwise  than 
common  solutions.  The  same  is  evidently  true  of  different 
albuminous  substances,  according  to  the  recent  investiga- 
tions of  Pauli.1  He  subjected  ox  or  horse  serum  to  dialysis 
for  a  very  long  time,  six  to  eight  weeks.  This  serum  did 
not  migrate  with  or  against  the  electric  current,  and  it  was 
not  precipitated  by  weak  solutions  of  alkaline  salts,  nor 
of  salts  of  zinc,  copper,  iron,  mercury,  or  lead.  It  was 
coagulated  by  strong  heat,  alcohol,  and  strong  solutions 
of  alkali  salts  or  zinc  sulphate.  These  sera  contain  two 
different  kinds  of  protein,  albumin  and  globulin.  These 
could  not  be  separated  by  means  of  the  current,  so  that 
neither  of  these  substances  was  carried  by  the  current. 
The  great  difference  between  the  so-called  organic  colloids 
and  the  inorganic  or  true  colloids  caused  Pauli  to  express 
the  opinion  that  we  should  not  attempt  to  deduce  the 
properties  of  organic  from  those  of  the  inorganic  colloids, 

1  W.  Pauli:  HofmeisUrs  Beitragc,  7.  531  (1906). 


EQUILIBRIA  IN  ABSORPTION  PROCESSES  161 

but  to  confine  our  studies  to  the  albuminous  substances 
if  we  wish  to  understand  the  processes  going  on  in  living 
matter.1 

One  of  the  properties  of  albuminous  substances  which 
was  regarded  as  proving  their  colloidal  nature  was  pre- 
cisely the  migration  of  these  substances  in  the  electric 
field.  Dialysed  serum,  says  Pauli,  does  not  migrate,  but 
if  we  add  an  acid,  the  egg-white  follows  the  positive  cur- 
rent ;  if  we  add  an  alkali  to  the  solution,  it  travels  to  the 
positive  side.  This  circumstance  is  explained  by  the 
adherents  of  the  colloidal  theory  by  the  assumption  that 
the  egg-white  absorbs  positive  H  ions  or  negative  OH  ions. 
As  Bredig,  Freundlich,  and  Loeb 2  have  remarked,  this 
follows  at  once  from  the  well-known  fact  that  proteins  are 
amphoteric  electrolytes,  which  form  salts  as  well  with 
acids  as  with  bases,  just  as  do  the  amido-acids,  e,g.  glyco- 
coll,  with  which  substances  the  albumins  are  even  very 
closely  related  according  to  the  recent  investigations  of 
Kossel  and  E.  Fischer.  It  is  quite  true  that,  just  as 
ammonia  by  adding  an  hydrogen  ion  forms  the  ammonium 
ion,  in  quite  the  same  manner  the  amido-group  of  the 
albuminous  substance  adds  hydrogen  and  gives  an  albumin 
ion.  But  there  is  a  very  great  difference  between  an  ion 
and  the  suspended  particles  (e.g.  of  kaolin)  which  obtain 
a  positive  change  through  the  influence  of  dielectric  forces. 
That  the  albuminous  substance  really  so  behaves,  that  it 
adds  a  hydrogen  ion  and  gives  an  albumin  ion,  —  i.e.  that 
the  addition  of  an  acid  to  it  gives  rise  to  a  real  neutralisa- 

1  Pauli  :  Naturiu.  Rundschau,  p.  3  (1906). 

2  Cf.    Loeb  :     Vorlesungen  iiber  die  Dynamik  der  Lebenscrschcinungen, 
pp.  65-67,  Leipzig  (1906). 


1 62  LECTURES  ON  IMMUNITY 

tion  phenomenon  like  that  of  ammonia,  —  is  evident  from 
Pauli's  investigations.  On  the  addition  of  acid  the  wander- 
ing of  the  albumen  to  the  cathode  at  first  increases  with 
the  quantity  of  acid  added,  and  then  reaches  a  maximal 
value.  The  stronger  hydrochloric  acid  has  a  greater  action 
than  the  weaker  acetic  acid.  Evidently  the  albuminous 
substance  has  the  character  of  a  weak  base  and  therefore 
the  formation  of  salt  is  greater  if  we  use  hydrochloric 
than  if  we  use  acetic  acid,  and  a  limit  of  the  wandering  is 
reached  when  the  substance  is  practically  neutralised. 

In  an  analogous  manner  the  sera  investigated  by  Pauli 
behave  with  alkalies.  The  wandering  to  the  anode  in- 
creases with  the  quantity  of  alkali  added,  until  a  limit  is 
reached.  In  this  case  evidently  no  hydroxyl  ions  are 
annexed  to  the  albuminous  substance,  but  instead  its  "acid" 
carboxyl  group  gives  off  a  hydrogen  ion  and  is  thereby 
itself  charged  negatively  as  an  albuminate  ion. 

Pauli  found  that  neutral  salts  do  not  give  a  charge  to 
the  serum,  but  KH2PO4,  which  has  an  acid  reaction,  and 
Na2HPO4,  Na3PO4,  NaHCO3,  and  Na2CO3,  which  have 
an  alkaline  reaction,  exert  an  influence  like  a  weak  acid  or 
as  weak  bases.  This  is  quite  clear  as  long  as  we  regard 
the  albuminous  substances  as  amphoteric  electrolytes ;  but 
if  we  regard  them  as  colloidal  particles,  we  cannot  predict 
anything  with  respect  to  the  influence  of  these  substances. 
It  is  quite  incomprehensible  how  this  latter  view  has  been 
so  often  preferred. 

The  behaviour  of  albumose,  pepton,  and  of  egg-white  as 
bases  has  been  very  thoroughly  investigated  by  Sjoqvist,1 

1  Sjoqvist  :  Skandinavisches  Archiv  f.  physioL  Chemie,  Bd.  V.,  p.  59 
(1895). 


EQUILIBRIA  IN  ABSORPTION  PROCESSES  163 

who  employed  for  this  purpose  his  method  of  study- 
ing the  conductivity.  Sjoqvist  stated  that  these  substances 
behave  quite  regularly  as  weak  bases.  The  "  mean " 
equivalent  weights  of  these  three  substances  were  found  to 
be  about  600,  250,  and  800  respectively.  The  egg-albumen 
was  a  base  about  six  times  weaker  than  aspartic  acid, 
but  about  nine  times  stronger  than  urea.  The  albumose 
(from  Schuchardt)  was  about  1.6  times  as  strong  a  base 
as  the  albumin.  Sjoqvist  investigated  the  neutralisa- 
tion of  these  bases  by  means  of  different  acids  as  hydro- 
chloric, sulphuric,  phosphoric,  and  lactic  acid,  and  found 
always  a  good  agreement  with  the  theoretical  view.  The 
amphoteric  properties  of  these  substances  have  also  been  the 
basis  for  investigations  on  the  action  of  pepsin  and  trypsin 
by  Sjoqvist,  Bayliss,  and  others  (cf.  pp.  65  and  79  above). 

A  property  of  the  antibodies,  which  recalls  the  tendency 
of  inorganic  colloids  to  precipitate  only  (or  chiefly)  colloids 
of  the  opposite  electric  sign,  is  their  specificity.  But 
whereas  the  positive  colloid  ferric  hydrate  is  attacked  by 
all  the  many  negative  colloids,  the  typhoid  bacilli  are  agglu- 
tinated only  by  typhoid  agglutinin.  Victor  Henri  has,  in 
association  with  his  students,  M.  Malloizel  and  Mme. 
Girard-Mangin,1  carried  out  some  experiments  on  agglutina- 
tion from  this  point  of  view.  He  found  that  red  blood- 
corpuscles  and  typhoid  bacilli  are,  as  most  substances 
suspended  in  water,  charged  negatively,  and  therefore  con- 
cluded that  these  cells  would  be  agglutinated  by  ferric 
hydrate,  as  Biltz  had  predicted.  He  found  that  this  really 

1  V.  Henri  et  L.  Malloizel  :  C.  R.  de  la  Soc.  de  BioL,  56.  I.  1073  (1904)  ; 
Mme.  Girard-Mangin  et  V.  Henri  :  C.  R.  de  la  Soc.  de  Biol.,  56.  II.  866, 
93L  933,  935.  936,  974  (i9<>4). 


1 64  LECTURES   ON  IMMUNITY 

occurs,  and  that  normal  serum  or  even  dissolved  starch 
has  a  somewhat  protecting  influence  against  the  agglutina- 
tion. But  later  on  M.  Henri  and  Mme.  Girard-Mangin 
investigated  the  influence  of  negative  colloids,  and  found 
that  they  had  precisely  the  same  agglutinating  influence 
as  the  positive  ones.  The  "colloidal  theory,"  therefore, 
has  proved  of  little  avail. 

That  proteins  are  able  to  combine  with  positive  ions,  not 
only  hydrogen,  but  even  potassium,  sodium,  or  calcium, 
has,  according  to  the  investigations  of  Pauli  and  Loeb,1  an 
extremely  great  importance  for  the  physiological  functions 
of  the  proteins. 

We  have  seen  in  the  chapter  on  the  velocity  of  reaction 
that  this  is  for  agglutinins  proportional  to  the  concentra- 
tion of  the  agglutinin  and  increases  with  temperature. 
From  this  we  concluded  that  the  agglutination  depends  on 
a  chemical  reaction  of  the  agglutinin  with  some  content  of 
the  bacterium.  In  his  excellent  work  on  microbiology 
Duclaux  2  shows  that  this  chemical  action  is  really  a  coagu- 
lation. He  cites  the  experiments  of  Kraus,  which  indicate 
that  the  filtrate  obtained  by  means  of  a  Chamberland  filter 
from  cultures  of  cholera  vibrios,  typhoid  or  pest-plague 
bacilli,  give  a  coagulum  with  their  specific  agglutinins.  He 
cites  further  the  experiments  of  Nicolle,  who  subjected  a  fil- 
trate from  macerated  coli  bacilli  to  an  agglutinin  obtained 
by  injecting  these  bacilli  into  the  veins  of  a  rabbit.  In  a 
mixture  of  ten  drops  of  the  filtrate  with  one  drop  of  the 
rabbit's  serum  there  appeared  after  some  hours  at  37°  a 
large  number  of  flocculent  bodies  that  resembled  to  a  very 

1  J.  Loeb  :  "  Studies  in  General  Physiology,"  Part  II,  544,  Chicago,  1905. 

2  Duclaux  :  "Traite  de  microbiologie,"  T.  II,  p.  706,  Paris,  1899. 


EQUILIBRIA  IN  ABSORPTION  PROCESSES  165 

high  degree  the  flocculation  in  a  culture  containing  living 
coli  bacilli  treated  with  the  same  agglutinin.  One  might 
replace  the  bacilli  with  some  fine  inert  powder,  e.g.  tal- 
cum ;  this  fine  powder  would  then,  just  like  the  bacilli,  be 
jammed  together  by  the  coagulum  in  their  neighbourhood. 
Therefore  the  deposits  containing  bacilli  are  more  volu- 
minous than  those  of  the  fluids  from  which  the  bacilli  are 
removed  by  filtering.  The  liquid  which  is  coagulated  by 
the  agglutinin  is  according  to  Nicolle  very  resistant  to  low 
and  high  temperatures.  It  is  soluble  in  alcohol  and  to  a 
certain  degree  in  ether,  so  that  an  extract  from  the  bacilli 
in  one  of  these  fluids  yields,  after  evaporation  to  dryness 
and  dissolution  in  a  weakly  alkaline  bouillon,  a  flocculent 
deposit  on  treatment  with  its  agglutinin. 

This  coagulable  substance  is  prepared  in  the  interior  of 
the  bacilli  which  contain  it,  and  it  is  even  partially  given 
up  to  the  surrounding  medium,  as  is  indicated  by  the 
experiments  of  Kraus.  Agglutinins  are  contained  in 
normal  sera,  as  for  instance  in  the  horse,  the  blood-serum 
of  which  agglutinates  cholera  vibrios  to  a  high  degree, 
and  less  effectively  cultures  of  Vibrio  Metschnikovi,  typhoid 
bacilli,  colon  bacilli,  and  tetanus  bacilli  as  well  as  strepto- 
coccus. The  normal  sera  of  different  animals  agglomerate 
the  normal  erythrocytes  of  other  animals,  as,  for  instance, 
the  serum  from  the  horse  agglutinates  erythrocytes  from 
guinea-pigs  or  rabbits.  In  these  cases,  just  as  with  the 
agglutinins  acting  upon  microbes,  it  is  possible  to  increase 
the  content  of  the  specific  agglutinin  in  the  normal  serum 
by  repeated  injections  of  the  erythrocytes  in  question. 

Even  simple  chemical  reagents  cause  an  agglutination 
of  bacilli,  thus,  for  instance,  typhoid  bacilli  are  agglutinated 


1 66  LECTURES  ON  IMMUNITY 

by  formaldehyde,  hydrogen  peroxid,  or  strong  alcohol. 
In  this  case  the  reagents  often  display  the  phenomenon 
that  a  greater  dosage  does  not  agglutinate,  whereas  a 
lesser  dose  produces  the  effect.  Acetic  acid  does  not 
agglutinate  some  cholera  vibrios  if  it  be  used  in  a  concen- 
tration of  o.i  per  cent,  but  has  a  strong  agglutinating 
effect  in  solutions  of  10  per  cent  only  to  lose  it  again  at 
a  strength  of  50  per  cent,  according  to  the  experiments  of 
Bossaert.  Mercuric  chlorid  agglutinates  in  a  concentra- 
tion of  only  0.3  per  cent  and  safranin  or  vesuvin  are  active 
at  a  concentration  of  0.05  per  cent.  Even  in  this  case 
different  bacilli  are  sensitive  to  a  different  degree;  thus, 
for  instance,  typhoid  bacilli  are  more  than  ten  times  as 
sensitive  to  safranin  as  colon  bacilli. 

If  the  action  of  the  agglutinin  be  a  coagulation  of  the 
contents  of  the  bacilli,  it  is  easy  to  understand  how  other 
coagulating  substances,  such  as  alcohol,  acids,  or  ura- 
nium acetate,  may  change  the  properties  of  the  bacilli  in 
nearly  the  same  manner  as  the  specific  agglutinin,  as 
results  from  the  experiments  of  Bechhold  cited  above. 
The  agglutinins  are  therefore  probably  only  a  special  class 
of  precipitins,  which  they  in  many  cases  even  resemble 
in  showing  optima  of  action  at  a  certain  concentration. 


CHAPTER  VI 

NEUTRALISATION   OF   THE   H^MOLYTIC   PROPERTIES 
OF   BASES   AND   OF   LYSINS   OF  BACTERIAL  ORIGIN 

THE  simplest  haemolytic  agents  are  the  bases  and  the 
acids.  Of  these  the  bases  exert  an  action  on  erythrocytes, 
which  is  very  similar  to  that  of  haemolysins  of  bacterial 
origin.  It  is  obvious  that  if  we  add  an  acid  to  an  alkaline 
solution  until  it  is  neutralised,  its  hasmolytic  action  will  be 
nullified.  In  some  few  cases,  as  for  instance  for  oleic  acid, 
this  is  not  true,  since  all  the  olein  derivatives  are  haemolytic 
agents,  which  salts  in  general  are  not. 

This  case  presents  the  closest  analogy  to  the  neutralisa- 
tion of  a  lysin,  e.g.  tetanolysin,  by  means  of  its  antilysin. 
At  first  sight  there  seems  to  be  a  difference,  since  any 
base  is  neutralised  by  any  acid,  whereas  the  antitetanoly- 
sin  is  a  perfect  specificum  against  tetanolysin  and  exerts 
no  neutralising  action  on  other  lysins.  But  this  difference 
is  more  apparent  than  real,  since  we  know  now  that  the 
acids  all  contain  hydrogen  ions  which  bind  the  hydroxyl 
ions,  common  to  all  bases. 

It  therefore  seemed  to  Madsen  and  myself  to  promise 
much  for  the  elucidation  of  the  phenomenon  of  neutralisa- 
tion of  lysins  by  their  antilysins  to  make  a  comparative 
study  of  the  common  neutralisation  of  a  base,  regarded 
as  a  haemolytic  agent,  with  that  of  a  lysin  and  its  anti- 
lysin. For  this  purpose  we  made  a  thorough  investign- 

167 


1 68  LECTURES  ON  IMMUNITY 

tion  of  the  action  of  bases,  acids,  and  salts  on  erythrocytes 
and  of  the  haemolytic  action  of  a  lysin,  namely,  tetanoly- 
sin,  in  the  presence  of  its  antilysin  and  of  different 
other  so-called  neutral  substances,  as  salts  and  different 
proteins.  The  tetanolysin  was  chosen  because  it  shows 
a  great  similarity  in  its  neutralisation  with  that  practically 
most  important  of  all  poisons,  namely,  the  diphtheria  poison. 
This  investigation  convinced  us  that  a  complete  analogy 
holds  for  the  two  phenomena  of  neutralisation,  that  of  a 
base,  for  instance,  ammonia,  and  that  of  tetanolysin.1 

If  we  add  different  bases,  for  instance,  ammonia  and 
sodium  hydrate,  to  red  blood-corpuscles,  we  find  that  the 
first  traces  of  alkali  are  without  any  haemolytic  effect  on 
the  cells.  This  first  ineffective  quantity  seems  to  be  bound 
by  the  blood-corpuscles  rather  strongly,  since  it  is,  within 
the  errors  of  observation,  proportional  to  the  quantity  of 
blood  used,  and  the  quantities  of  sodium  hydrate  and  of 
ammonia  bound  by  the  same  quantity  of  blood-corpuscles 
are  chemically  equivalent  (cf.  p.  no).  On  the  addition  of 
greater  quantities  of  alkali  a  very  weak  haemolysis  occurs ; 
the  fluid  is  only  faint  yellow.  As  the  quantity  of  alkali 
increases,  the  haemolysed  quantity  of  the  red  blood-corpus- 
cles increases  very  rapidly  and  often  nearly  proportion- 
ally to  the  square  of  the  unbound  quantity  of  alkali.  This 
proceeds  until  the  haemolysis  is  total,  that  is,  until  all  the 
red  blood-corpuscles  have  given  up  their  haemoglobin  to 
the  surrounding  medium.  After  this  a  further  addition  of 
alkali  produces  no  change  in  the  quantity  of  haemolysis, 
though  the  velocity  of  reaction  is  increased.  The  state- 

1  Arrhenius  and  Madsen :  Festskrift,  Copenhagen,  No.  3,  1902  ;  Zeitschr* 
f.ph.  a.,  44.  7  (1903). 


NEUTRALISATION  OF  H^EMOLYSINS 


169 


ment  is  valid  also  for  the  action  of  such  hsemolysins  as 
tetanolysin.  It  seems  as  if  also  in  this  case  a  chemical 
binding  takes  place,  but  the  compound  seems  to  be  to  a 
higher  degree  dissociated,  so  that  the  limit  is  not  so  sharp 
as  for  the  alkalies. 

To  give  an  idea  of  this  process  I  reproduce  here  some 
figures  for  the  haemolytic  action  of  taurocholate  of  so- 
dium, saponin,  potassium  hydrate,  and  solanin.  For  potas- 
sium hydrate  2.5  per  cent  suspensions  of  bovine  corpuscles, 
for  the  other  haemolysins  2  per  cent  suspensions  of  equine 
erythrocytes,  were  used.  Following  the  addition  of  the 
suspension  of  cells  to  the  poison,  the  mixture  was  shaken 
and  then  for  one  hour  placed  in  an  incubator  of  37°  C.  and 
after  this  eighteen  hours  in  a  refrigerator  and  then  com- 
pared with  the  solutions  of  haemoglobin  of  different  concen- 
trations prepared  by  the  haemolysis  of  different  quantities 
of  the  same  blood-corpuscles  by  pure  water.  The  concen- 
tration is  given  for  the  potassium  hydrate  in  fractions  of  a 
normal  solution,  for  the  other  substances  in  fractions  of 
the  whole  fluid  (weight  of  dissolved  substance :  weight  of 
solution). 


SAPONIN 

TAUROCHOLATE  OF  SODIUM 

Cone.  C  '  io6 

H 

K-  io-5 

Cone.  C«io» 

H 

K.  io-s 

40 

go 

2.35 

I40 

91 

6.81 

28 

40 

2.26 

IOO 

55 

7.41 

20 

IO 

1.58 

68 

18 

6.24 

H 

5 

l.6o 

48 

4 

4.17 

10 

3 

i-73 

32 

2-5 

4-94 

7 

2 

2.02 

20 

i-3 

5.70 

LECTURES  ON  IMMUNITY 


POTASSIUM  HYDRATE 

SOLANIN 

Cone.  C  •  io5 

H 

K.  10-3 

Cone.  C'io8 

H 

K-  io-s 

62.5 

27 

8.3I 

40 

86 

2.32 

5° 

13 

7.21 

28 

70 

2.98 

37-5 

4 

5-33 

20 

4 

1.  00 

3i-S 

3-5 

5.98 

H 

2.4 

I.  II 

25 

2 

5.66 

10 

'•5 

i-5 

As  will  be  seen  from  these  figures,  these  poisons  do  not 
follow  nearly  as  closely  as  tetanolysin  and  ammonia  the 
rule  that  the  square  root  of  the  degree  of  haemolysis  is 
proportional  to  the  concentration.  The  quotient  of  these 
two  magnitudes  is  tabulated  under  K.  In  general  the 
greater  the  velocity  of  reaction  the  more  marked  is  the 
deviation  from  the  said  rule.  At  about  10  per  cent 
the  haemolysis  increases  relatively  more  rapidly  with  the 
concentration  than  at  other  degrees  of  haemolysis.  There- 
fore the  measurement  of  the  quantity  of  poison  present  by 
means  of  the  haemolytic  determination  has  the  greatest 
exactitude  in  the  neighbourhood  of  this  point. 

Different  strong  monovalent  bases  act  in  equivalent 
quantities  nearly  to  the  same  degree  upon  the  blood- 
corpuscles.  The  divalent  bases  Ca(OH)2  and  Ba(OH)2 
seem  to  give  some  solid  precipitate  in  the  erythrocytes, 
which  hinders  measurements,  at  least  at  higher  concentra- 
tions. The  haemolysis  observed  is  then  nearly  independent 
of  the  quantity  of  base  added.  Ammonia  also  has  nearly 
the  same  strength  of  action  as  equivalent  quantities  of  the 
strong  monovalent  bases.  Sometimes  (for  low  concentra- 
tions of  blood)  its  action  is  a  little  less,  in  other  cases  (at 


NEUTRALISATION  OF   H^EMOLYSINS  1 7 1 

higher  concentrations  of  blood)  it  is  somewhat  greater 
than  that  of  the  stronger  bases,  at  least  after  a  prolonged 
time  of  reaction  (cf.  p.  in).  This  seems  to  indicate  that 
some  compound  is  formed,  so  that  the  equivalent  quan- 
tities act  to  the  same  degree,  but  that  the  ammonia  com- 
pound is  to  some  degree  hydrolysed,  which  causes  the 
deviations. 

Acids  also  destroy  the  red  blood-corpuscles,  but  this 
phenomenon  has  an  appearance  somewhat  different  from 
the  haemolysis  by  means  of  bases.  Following  the  action 
of  the  alkalies  and  also  of  the  lysins  of  bacterial  origin, 
the  fluid  surrounding  the  blood-corpuscles  takes  up  their 
intensive  purple  colouring  matter  and  assumes  the  charac- 
teristic red  colour  of  blood.  The  acids,  on  the  other  hand, 
alter  the  colouring  matter,  so  that  the  fluid  becomes  dark 
brown,  and  after  shaking  the  foam  persists  often  for  forty- 
eight  hours  or  more.  This  indicates  a  coagulating  influ- 
ence. With  lower  degrees  of  haemolysis  by  acids  the  fluid 
has,  however,  also  a  reddish  tint.  At  the  same  time  a 
strong  agglutination  of  the  blood-corpuscles  is  perceptible. 
At  higher  concentrations  large  clumps  are  formed,  remind- 
ing one  somewhat  of  the  flocculent  precipitates  of  alumin- 
ium salts  mixed  with  an  alkali.  The  degree  of  haemolysis 
by  a  strong  acid  is  about  as  pronounced  as  that  of  three 
to  four  times  the  equivalent  quantity  of  a  strong  base. 
Equivalent  quantities  of  different  acids  (hydrochloric,  sul- 
phuric, oxalic,  tartaric,  citric,  and  acetic)  act  nearly  to  the 
same  degree,  the  weaker  acids  (for  instance,  acetic  acid) 
act  a  little  slower  than  the  stronger ;  and  extremely  weak 
acids,  as  boracic  acid,  exert  no  appreciable  haemolytic 
action  (the  same  is  probably  valid  for  extremely  weak 


1^2  LECTURES  ON  IMMUNITY 

bases),  probably  because  the  process  goes  on  with  insen- 
sible velocity. 

For  stronger  concentrations  of  the  haemolysins  total 
haemolysis  occurs  if  they  are  permitted  to  act  through  a 
long  enough  time.  If  the  time  of  action  be  restricted  (as 
by  centrifugation),  it  is  possible  to  follow  the  development 
of  the  reaction,  as  has  been  said  above  (cf.  p.  100). 

The  presence  of  salt J  exerts  a  strong  retardative  influ- 
ence upon  the  hasmolytic  power  of  the  alkalies.  Probably 
this  effect  depends  on  a  diminution  of  the  velocity  of  re- 
action. Especially  is  this  true  for  the  influence  of  ammo- 
niacal  salts  upon  ammonia.  The  different  salts  of  the 
strong  bases  (KOH,  NaOH,  and  LiOH)  are  of  the  same 
degree  of  efficacy  in  equivalent  concentrations;  the  effect 
is  nearly  proportional  to  the  cube  root  of  the  concentra- 
tion ;  0.02  n.  salt  solution  lowers  the  effect  in  the  propor- 
tions i  :  0.4.  The  salts  of  ammonia  also  seem  to  be  very 
similar  to  each  other  in  this  regard  :  0.004 n-  NH3  salt 
lowers  the  effect  in  the  proportion  1:0.7;  o.oi6n.  in  the 
proportion  1:0.25  ;  and  0.06  n.  in  the  proportion  1:0.14. 

On  the  other  hand,  it  is  perfectly  clear  that  the  addition 
of  the  equivalent  quantity  of  hydrochloric  acid  to  a  solu- 
tion of  sodium  hydrate  would  completely  suspend  its  hae- 
molytic  power,  since  in  this  reaction  sodium  chloride  is 
formed,  which  has  no  haemolytic  effect.  Of  a  sodium 
hydrate  solution  (neutralised  to  50  per  cent)  it  would  be 
necessary  to  add  the  double  quantity  (a  slight  correction 
should  be  introduced  for  the  lowering  influence  of  the 
salt,  and  for  the  quantity  of  alkali  bound  that  gives  no 
action)  to  attain  the  same  haemolytic  effect.  We  then  say 

1  In  this  case  the  physiological  solution  is  made  of  cane  sugar. 


NEUTRALISATION   OF  H^MOLYSINS  173 

that  the  toxicity  of  the  first  solution  is  half  as  great  as  that 
of  the  second  solution.  The  effect  of  the  neutralisation  of 
the  sodium  hydrate  by  the  addition  of  hydrochloric  acid 
may  therefore  be  graphically  represented  in  the  following 
figure  by  the  line  AB.  The  toxicity  is  here  ordinates,  and 
the  quantity  of  acid  added  is  abscissae.  This  line  would 
be  a  straight  line  if  the  effect  of  the  salt  did  not  produce  a 
perturbing  influence. 

When  we  have  added  the  acid  necessary  to  neutralise 
the  free  alkali  (point  B\  we  have  still  to  add  a  small  quan- 
tity to  neutralise  the  alkali  bound  in  the  erythrocytes,  and 
then  further  add  a  small  quantity  of  acid  before  the  solu- 
tion is  strong  enough  in  acid  to  give  haemolysis  again. 
These  portions  are  represented  by  the  parts  BC  and  CD 
in  the  diagram.  On  the  addition  of  more  acid  to  the  solu- 


u  BC   D 

FIG.  i. 

tion  its  toxicity  increases  nearly  proportionally  to  the 
quantity  of  free  acid  (neither  bound  to  the  alkali,  nor  in 
the  erythrocytes).  This  toxicity  is  represented  by  the  al- 
most straight  line  DE. 

In  quite  the  same  manner  the  toxicity  changes  on  the 


174 


LECTURES  ON  IMMUNITY 


addition  of  a  strong  acid  to  a  solution  of  ammonia.  The 
line  AB  then  deviates  a  little  more,  but  not  very  much, 
from  a  straight  line,  according  to  the  relatively  strong  in- 
fluence of  the  ammonium  salts.  The  real  curve  would  lie 
little  below  AB. 


FIG.  2. 

Now,  if  we  add  to  the  ammonia-solution  a  very  weak 
acid,  such  as  boracic  acid,  which  has  no  sensible  haemo- 
lytic  action,  the  phenomenon  will  behave  in  a  rather  differ- 
ent manner,  in  consequence  of  the  hydrolytic  effect  of  the 
water.  The  hydrolysis  results  in  this,  that  there  always  re- 
mains a  certain  quantity  of  free  ammonia,  even  if  we  add 
as  large  quantities  of  boracic  acid  as  possible  (up  to  satu- 
ration). Then  the  curve  representing  the  toxicity  de- 
scends as  the  quantity  of  boracic  acid  added  increases,  but 
never  reaches  zero,  as  is  indicated  on  Fig.  2.  The 
quantity  (q)  of  free  ammonia  may  be  calculated  according 
to  the  equation :  — 


NEUTRALISATION  OF  H^MOLYSINS 


where  a  is  the  quantity  of  ammonia  present  from  the  be- 
ginning, before  boracic  acid  was  added,  q  the  quantity  of 
free  un-neutralised  ammonia,  n  is  the  added  quantity 
of  this  acid,  consequently  (a  —  <f)  the  quantity  of  salt 
formed,  and  \n  —  (a  —  q)\  the  quantity  of  free  boracic 
acid.  The  quantities  should  be  expressed  in  equivalents, 
and  one  molecule  of  NH3  is  found  to  be  equivalent  to  one 


0  0.5  i.  1.5  2.X 

FIG.  3. 

molecule  of  H3O3B.  The  constant  K  has  a  value  depend- 
ent on  the  temperature.  The  last  equation  is  a  form  of 
the  equation  expressing  the  law  of  Guldberg  and  Waage. 
A  special  theoretical  investigation  showed  that  it  might  be 
employed  in  this  case. 

Now  the  toxicity  is  proportional  to  the  concentration  of 
free  ammonia,  though  in  this  case  a  correction  must  be  in- 
troduced for  the  lowering  action  of  the  ammonium  salt,  as 
indicated  by  experiments  on  this  action.  Therefore,  if  we 


LECTURES  ON  IMMUNITY 


carry  out  experiments  on  the  toxicity  of  ammonia  with  the 
addition  of  different  quantities  of  boracic  acid,  this  toxicity 
may  be  calculated  according  to  the  equation  cited.  On 
the  other  hand,  this  toxicity  may  be  determined  directly 
from  the  haemolytic  power.  In  this  case  we  suppose  that 
the  quantity  of  ammonia  absorbed  by  the  erythrocytes 
may  be  neglected  (cf.  p.  no).  The  comparison  between 
the  results  of  observation  and  calculation  (K=i.O2)  is 
given  in  the  following  table  : l  — 

TOXICITY  (^)  OF  o.i  N.  NH3  (i  EQUIVALENT)  WITH  n  EQUIVALENTS 
OF  BORACIC  ACID 


«  = 

?obs. 

?calc. 

A?obs. 

0 

100 

(100) 

0.17 

85 

79 

15 

0.33 

69 

64 

16 

0.67 

43 

42 

26  12=13 

I 

25 

27 

18  :  2=  9 

1.33 

20 

18 

5=2] 

1.67 

13 

13 

7:2     2.5 

2 

10 

10 

3^J 

The  agreement  between  the  observed  and  calculated  values 
of  q  is  quite  within  the  limits  of  the  errors  of  observation. 
Under  A^obs>  is  tabulated  the  quantity  of  ammonia  which 
is  neutralised  with  regard  to  its  haemolytic  power  by  the  ad- 
dition of  the  sixth  part  of  one  equivalent  of  boracic  acid. 
The  two  first  additions  lower  the  toxicity  by  nearly  the  same 
amount  (16.7  per  cent)  as  a  strong  acid.  The  portions 
between  one  and  two  thirds  and  between  two  and  three 
thirds  have  a  noticeably  lower  influence  (about  £  and  f  re- 

1  According  to  a  recent  investigation  by  H.  Lunden  on  the  hydrolysis  of 
ammonium -borate  the  constant  K  is  1.02  in  complete  agreement  with  the 
value  given  above  as  results  of  experiments  on  hydrolysis. 


NEUTRALISATION  OF  H^MOLYSINS  1/7 

spectively).  The  next  equivalent  of  boracic  acid  added  has 
an  effect  which  equals  only  about  the  fifth  part  of  that  of 
the  first  equivalent. 

This  behaviour  is  to  a  high  degree  similar  to  that  termed 
Ehrlich's  phenomenon,  observed  in  the  neutralisation  of  a 
toxin  with  its  antitoxin.  The  first  part  of  the  antitoxin 
added  neutralises,  generally  speaking,  a  greater  portion 
of  the  toxin  than  does  the  second  equal  addition,  this  a 
greater  one  than  the  third,  and  so  forth.  To  explain  this 
peculiarity  (of  diphtheria-toxin)  Ehrlich  supposes  that  the 
toxin  is  a  mixture  of  many  different  "  partial  toxins,"  which 
possess  different  degrees  of  toxicity  in  equivalent  quantities, 
and  have  a  different  affinity  for  antitoxin.  If  antitoxin 
be  added,  it  at  first  neutralises  that  part  of  the  poison 
which  has  the  greatest  affinity,  and  which  also  is  the 
strongest  poison ;  thereafter  that  with  the'  next  greatest 
affinity,  which  also  is  the  second  in  toxic  strength,  and 
so  forth.  At  the  end  the  very  weakest  portions  appear 
for  neutralisation.  Ehrlich  designated  these  hypothetical 
"  partial  poisons "  with  names  coined  from  the  Greek 
language,  as  prototoxin,  deuterotoxin,  tritotoxin,  epitoxin, 
etc. 

If  we  apply  Ehrlich's  views  to  ammonia,  this  substance 
should,  according  to  the  experiment  of  neutralisation  by 
boric  acid,  be  composed  of  different  "  partial  ammonias," 
of  which  the  strongest  one  should  be  neutralised  first, 
the  second  strongest  next,  etc.  Of  course  this  compli- 
cated explanation  cannot  possibly  be  used  for  ammonia, 
which  we  know  is  a  very  simple  chemical  compound  of 
high  purity,  but  it  was  by  Ehrlich  and  his  pupils  applied 
to  other  poisons  quite  generally,  e.g.  to  diphtheria-poison 


178 


LECTURES  ON  IMMUNITY 


and  tetanolysin,  which,  on  neutralisation,  as  we  shall  soon 
see,  behave  in  a  manner  very  similar  to  ammonia. 

The  following  figures,  found  for  the  toxicity  of  tetanolysin 
after  the  addition  of  different  quantities  of  antitoxin,  may 
serve  as  an  example.  It  is  illustrated  by  Fig.  3.  This 
curve  has  a  tangent  at  its  beginning,  which  cuts  the  ^r-axis 
in  the  point  x  =0.276,  indicating  that  if  the  neutralisation 
proceeded  according  to  the  same  laws  as  hold  for  the  neu- 
tralisation of  strong  acids  by  strong  bases,  i.e.  if  the  quan- 
tity neutralised  was  proportional  to  the  antitoxin  added 
until  total  neutralisation  was  reached,  then  0.276  parts 
(c.c.)  of  the  unit  of  antitoxin  used  would  neutralise  com- 
pletely the  quantity  of  toxin  used  (2  c.c.  of  a  2  per  cent 
solution).  In  other  words,  these  quantities  are  equivalent. 
By  the  aid  of  this  value  the  quantities  (n)  of  antitoxins  are 
calculated  in  the  following  table  in  equivalents  («x)  of  the 
toxin  present  taken  as  unit :  — 

TOXICITY  (?)  OF  TETANOLYSIN  AFTER  ADDITION  OF  n  c.c.  OF  ANTILYSIN 


n 

*l 

fobs. 

?calc. 

0 

0 

IOO 

IOO 

0.05 

0.18 

82 

82 

O.I 

0.36 

7° 

66 

0.15 

°-54 

52 

52 

0.2 

0.72 

36 

38 

0-3 

1.09 

22 

23 

0.4 

1-45 

14.2 

13-9 

0.5 

1.81 

10.  1 

10.4 

0.7 

2-54 

6.1 

6.3 

1.0 

3.26 

4.0 

4.0 

1.3 

4-35 

2.7 

2.9 

1.6 

5-44 

2.0 

2-5 

2.O 

6.52 

1.8 

1.9 

NEUTRALISATION  OF  H^MOLYSINS  1/9 

The  values  calculated  are  derived  with  the  aid  of  the  same 
equation  as  given  above  for  ammonia,  with  the  constant 
o.  1 1 5.  The  experiments  were  so  executed  that  the  mixture 
of  toxin  and  antitoxin  were  left  at  20°  C.  for  two  hours ; 
thereupon  they  were  mixed  with  the  suspension  of  erythro- 
cytes  (2.5  per  cent  horse  blood)  and  for  one  hour  held  in 
a  thermostat  at  37°.  The  degree  of  haemolysis  was  deter- 
mined as  described  above  (cf.  p.  15).  The  constant 
0.115  is  therefore  valid  at  20°  C.  In  these  and  similar 
experiments  it  is  assumed  that  the  absorption  of  the  poison 
in  the  erythrocytes  may  be  neglected. 

The  antitoxin  used  was  a  solution  containing  0.0025  per 
cent  (per  c.c.)  of  the  content  of  antitoxin  in  a  standard 
solution.  This  fact  indicates  that  the  original  blood-serum 
containing  the  antitoxin  derived  from  a  horse  injected 
with  tetanus  poison  contained  in  one  c.c.  nearly  5800  times 
as  much  antitoxin  as  that  which  was  equivalent  to  the 
quantity  of  poison  contained  in  one  gram  of  the  dried  teta- 
nus preparation  prepared  by  precipitation  from  a  strong 
tetanus  bouillon  with  ammonium  sulphate.  From  this 
figure  it  is  easy  to  see  that  the  injected  horse  held  in  its 
blood  (about  50 1.)  many  (about  1 5)  million  times  the  equiva- 
lent quantity  of  the  injected  poison  (about  20  g. ;  some- 
times this  quantity  may  be  still  less).  This  circumstance 
deters  us  from  accepting  an  idea  which  seemed  at  first 
rather  probable  —  it  was  suggested  by  Behring  —  that 
the  antitoxin  is  a  derivative  of  the  injected  toxin.  To  sim- 
ilar results  have  led  the  experiments  on  the  production  of 
diptheria-antitoxin.  If  the  antitoxin  produced  did  not  ex- 
ceed many  times  the  poison  used  for  its  production,  the  prep- 
aration of  antitoxin  would  evidently  have  no  practical  value. 


I  So  LECTURES  ON  IMMUNITY 

The  curve  which  represents  the  experiments  of  Madsen 
on  tetanolysin  resembles  very  much  that  representing  the 
neutralisation  of  ammonia  by  means  of  boracic  acid.  It  is 
convex  to  the  ;r-axis,  which  it  never  reaches.  This  prop- 
erty indicates  that  the  greater  the  quantity  added,  the 
less  is  also  the  neutralising  power  of  the  same  quantity 
of  antitoxin.  But  there  is  no  reason  to  explain  this 
peculiarity  by  the  hypothesis  of  Ehrlich,  that  in  the  toxic 
solution  exist  side  by  side  a  large  number  of  poisons. 

The  equation  which  we  used  for  the  calculation  of  the 
results,  and  which  coincides  very  well  with  the  experiment, 
has  the  following  form  :  — 
(Quantity  of  free  lysin)  x  (guantity  of  free  antitoxin)  -j*~ 

K  (quantity  of  bound  toxin2). 

According  to  the  laws  of  physical  chemistry  this  equa- 
tion indicates  that  of  one  molecule  of  toxin  and  one 
molecule  of  antitoxin  there  are  formed  two  molecules  of 
the  reaction-products. 

This  reaction  is  therefore  rather  similar  to  that  of  alco- 
hol and  acid  to  give  ester  and  water,  one  molecule  of  each 
substance  entering  into  the  chemical  equation  of  reaction. 
In  this  case,  if  equivalent  quantities  of  the  reagents  are 
used,  two-thirds  of  them  are  transformed  to  ester  and 
water,  when  the  equilibrium  is  reached.  The  constant  K 
is  in  this  case  ^=0.25,  about  the  double  of  that  found  for 
tetanolysin. 

The  constant  K  of  the  equation  of  equilibrium  is  altered 
with  temperature.  When  Madsen  and  I  investigated  this 
phenomenon  for  the  first  time,  we  found  a  very  great 
increase  in  the  proportion  of  i  :  4.7  for  the  interval  of  tem- 
perature 20  to  37.3  degrees.  Later  experiments  have 


NEUTRALISATION  OF  H^EMOLYSINS  l8l 

given  a  much  smaller  value  of  the  increase,  which  amounts 
only  to  the  proportion  i  :  1.91  between  16  and  37°  C.1  A 
great  difficulty  inherent  in  the  determination  of  the  con- 
stants of  tetanolysin,  as  well  as  of  other  poisons,  lies  in  the 
circumstance  that  the  constant  of  equilibrium  is  rather  dif- 
ferent for  different  preparations  of  the  poison.  Fresh 
specimens  of  tetanolysin  seem  to  give  lower  constants 
than  old  ones.  In  general  the  constant  of  fresh  teta- 
nolysin seems  to  lie  rather  near  to  0.12  at  20°  C.  (room 
temperature). 

From  the  variation  of  K  with  temperature  it  is  possible 
to  calculate  the  heat  of  reaction  which  is  developed  in  the 
combination  of  one  grammolecule  of  tetanolysin  with  one 
of  antitoxin  to  form  two  of  the  reaction-products.  A 
change  in  the  proportion  of  I  :  1.91  in  the  interval  be- 
tween 1 6  and  37°  C.  corresponds  to  a  development  of 
5480  calories. 

As  we  have  seen  above  (cf.  p.  41),  tetanolysin  is  rap- 
idly decomposed  in  temperatures  in  the  neighbourhood 
of  50°.  An  elevation  of  the  temperature  of  3.7  degrees 
increases  the  constant  of  velocity  in  the  proportion  16.8  : 1. 
At  49.8°  C.  the  rate  of  destruction  is  of  such  a  magnitude 
that  a  poisonous  solution  loses  half  its  strength  in  62  min- 
utes. From  these  it  is  easy  to  calculate  that  at  20.2  and 
5.4  degrees  it  will  require  6.6  xio9  and  5.3  x  io14  hours 
(i.e.  7.5  x  io5  and  6.2  x  io10  years)  respectively  to  descend  to 
half  its  strength.  Now  it  is  often  observed  that  solutions 
of  tetanolysin  weaken  very  rapidly,  thus,  for  instance,  it  may 
lose  about  five-sixths  of  its  haemolytic  power  within  five  days 

iMadsen  and  Arrhenius:  Medd.  fr.  Vet.~Ak  :  s.  Nobelinstitut,  1.  No.  3, 
5 


1 82  LECTURES  ON  IMMUNITY 

at  20°  C.  (as  Madsen  and  I  observed  in  1902);  and  dried 
toxin  lost  in  two  years  on  storage  in  a  cold  room  (of  about 
6°  C.)  two-thirds  of  its  haemolytic  power.  This  destruction 
is  evidently  of  a  wholly  different  nature  from  that  observed 
at  50°  C.,  which  would  be  entirely  imperceptible  at  6  and 
20°  C.  respectively.  In  the  solutions  at  room  temperature 
it  is  perhaps  bacteria  (e.g.  Bacillus  pyocyaneus}  or  the 
influence  of  dissolved  glass  which  cause  the  rapid  destruc- 
tion ;  in  the  dried  tetanolysin  other  slow  chemical  processes 
may  be  responsible  for  the  loss  of  haemolytic  action. 

The  peculiar  observation  is  here  made  that  during  this 
destruction  the  power  of  binding  antilysin  does  not 
decrease  at  the  same  rate  as  the  haemolytic  activity. 
Sometimes  no  decrease  of  the  antitoxin-binding  faculty  is 
observed  at  all,  so  that  solutions  of  lysin  and  antilysin, 
that  were  equivalent  immediately  after  their  union,  also 
remain  equivalent  after  the  deterioration  of  the  poison. 
On  this  ground  Ehrlich  concluded  that  the  lysin  is  trans- 
formed into  an  innocuous,  or  nearly  innocuous,  modifica- 
tion, which  retains  the  properties  of  neutralisation  of  the 
antitoxin  characteristic  of  the  original  poison.  This  sub- 
stance is  termed  by  Ehrlich  the  toxoid.  The  toxoid  not 
only  seems  to  be  equivalent  with  the  poison,  but  also  to 
possess  nearly  the  same  constant  of  equilibrium.  And 
even  one  of  the  reaction-products  of  the  toxoid  with  the 
antitoxin  seems  to  be  identical  with  one  of  the  products 
of  the  corresponding  reaction  of  the  toxin.  Only  in  this 
manner  is  it  possible  to  explain  that  the  neutralisation 
curve  of  the  attenuated  toxin  is  very  similar  to  that  of  the 
original  toxin.  It  may,  on  the  other  hand,  be  recalled  that 
the  equilibrium-constant  of  old  tetanolysin  preparations 


NEUTRALISATION  OF  H^MOLYSINS  183 

has  been  found  to  have  a  very  high  value  and  to  change 
greatly  with  temperature,  so  that  evidently  here  greater 
transformations  take  place  during  the  course  of  time. 

In  order  to  explain  this  peculiarity  of  the  toxin,  Ehrlich 
originated  his  so-called  side  chain  theory,  which  has 
played  a  great  role  in  these  matters,  especially  in  the 
German  literature.  Organic  chemistry  teaches  us  that 
certain  properties  of  different  substances,  for  instance  the 
property  of  giving  coloured  solutions,  depend  upon  the 
presence  in  these  substances  of  the  same  group  of  atoms ; 
in  this  special  case  this  group  is  called  the  chromophoric 
group.  The  other  parts  of  the  molecule  may  be  rather 
different  in  the  different  substances  with  the  same  prop- 
erty, and  therefore  this  function  is  considered  to  be, 
so  to  speak,  located  in  the  common  group.  Now  the 
poisons  possess  the  two  common  properties  of  being 
poisonous  and  of  binding  their  antitoxins,  and  these  two 
properties  do  not  vary  with  each  other ;  as  we  have  seen, 
the  poisonous  attribute  diminishes  more  rapidly  than  the 
other  in  a  solution  of  tetanolysin,  and  the  same  is  the  case 
with  diphtheria-toxin,  the  study  of  which  led  Ehrlich  to  his 
conceptions.  Ehrlich  therefore  expresses  this  peculiarity 
in  the  following  manner.  The  two  said  properties  belong 
to  two  different  groups,  called  the  toxophoric  group,  which 
is  poisonous,  and  the  haptophoric  group,  which  binds  anti- 
toxin. In  the  molecule  of  the  poisonous  substance,  which 
we  suppose  to  be  composed  of  very  many  atoms,  the  two 
groups  lie  rather  far  from  each  other,  so  that  chemical 
changes  may  take  place  in  the  one  group  —  the  toxophoric 
—  without  influencing  sensibly  the  function  of  the  other 
group.  To  express  this  Ehrlich  supposes  that  the  two 


1 84  LECTURES  ON  IMMUNITY 

groups  are  bound  to  the  central  part  of  the  molecule  as 
side  chains,  known  from  the  chemistry  of  the  benzene 
derivatives.  If  now,  as  is  often  observed,  no  other  change 
of  the  poison  takes  place  than  that  its  toxicity  diminishes 
in  a  certain  ratio,  e.g.  to  50  per  cent,  then  to  explain  this 
peculiarity,  Ehrlich  must  assume  that  all  the  partial  poisons 
are  weakened  to  the  same  degree,  which  seems  very  im- 
probable. From  our  point  of  view  we  might  explain  the 
same  fact  by  saying  that  the  constant  of  equilibrium  in 
the  above  equation  has  not  been  "  sensibly  "  altered  by  the 
change  in  the  toxophoric  group.  This  is  quite  possible, 
although  experience  with  the  constant  of  equilibrium,  the 
so-called  dissociation-constant,  in  acids  teaches  us  that 
it  is  rather  sensible  to  changes  in  the  molecule.  But  the 
great  distance  between  the  different  groups  in  the  poison- 
ous molecule  may  have  the  effect  that  such  an  influence 
is  in  this  case  insensible.1 

There  is  another  possible  explanation  of  the  phenomenon. 
As  will  be  seen  in  Chapter  VIII,  many  poisons  are  com- 
pounds of  two  different  substances.  It  is  possible  to  sup- 
pose that  even  the  so-called  simple  poisons  are  compounds 
of  two  substances,  of  which  the  one  corresponding  to  the 
haptophoric  group  is  bound  by  antitoxin.  If  this  antitoxin 
binding  property  of  the  poison  is  relatively  stable  and 
present  in  great  excess,  and  if  the  poisonous  compound  is 
formed  of  one  molecule  of  each  constituent,  and  is  a  highly 
dissociable  substance,  its  quantity  will  be  proportional  to 
the  concentrations  of  the  two  constituents.  Then,  evi- 
dently, the  constant  of  equilibrium  would  remain  unaltered 
if  the  group  that  does  not  bind  antitoxin  slowly  disappears, 

lCf.  Ostwald:  Ztitschr.f.  ph.  Ch.,  3.  374  (] 


NEUTRALISATION  OF  ILEMOLYSINS  1 8$ 

and  we  would  expect  just  the  phenomenon  actually  ob- 
served. In  order  to  avoid  unnecessary  changes  we  may, 
until  future  experiments  decide  the  question,  employ  the 
hypothesis  that  the  poisonous  molecules  possess  two 
groups,  the  one  toxophorous  and  rather  labile,  the  other 
haptophorous  and  more  stable. 

It  is  not  necessary  that  the  compound  poison  should 
exist  to  a  sensible  degree.  We  have,  for  instance  (cf. 
p.  74),  seen  that  the  velocity  of  coagulation  of  casein  is  pro- 
portional as  well  to  the  rennet  present  as  to  the  concentra- 
tion of  the  calcium  ions.  As  has  been  made  probable  by 
Fuld  and  Spiro,  the  "  antirennet "  contained  in  normal 
horse-serum  acts  so  that  it  binds  the  calcium  ions  ;  before 
this  research,  however,  it  was  supposed  that  the  serum 
neutralised  (bound)  the  rennet.  In  this  case  it  is  possible 
to  destroy  the  rennet  by  heating  to  60°  C.  At  lower  tem- 
peratures (30°  or  so)  it  weakens  slowly ;  but  the  calcium 
ions,  we  may  suppose,  remain  unaltered.  The  rennet 
evidently  corresponds  to  the  toxophorous  group,  the  cal- 
cium ions  to  the  haptophorous  group  of  a  toxin,  and  the 
serum  to  the  antitoxin.  Evidently  the  binding  of  the  cal- 
cium ions  by  the  serum  will  be  independent  of  the  quantity 
of  rennet  present.  Therefore  we  may  say  of  the  combina- 
tion, rennet-calcium-ions,  that  its  antitoxin  binding  property 
remains  unchanged,  while  its  toxic  (coagulating)  property 
diminishes  with  time.  Such  a  point  of  view  has  obviously 
a  great  advantage  over  that  of  Ehrlich ;  but  in  favour  of 
the  continuous  development  of  the  science,  it  seems  rea- 
sonable to  retain  for  this  case  the  nomenclature  of  Ehrlich, 
provided  that  no  far-reaching  theoretical  developments  are 
based  upon  it  —  at  least  until  the  decomposition  of  toxins 


1 86 


LECTURES  ON   IMMUNITY 


into  their  two  constituents  has  been  proved  for  more  cases 
than  the  coagulating  action  of  rennet  (and  other  casein- 
coagulating  substances,  lactoserum  included,  cf.  Chapter 
IX). 

Just  in  the  same  manner  as  tetanolysin  behave  other 
lysins  of  bacterial  origin.  For  streptolysin  produced  by 
streptococcus  Madsen  and  Walbum  have  found  the  follow- 
ing figures  of  the  toxicity  (q),  after  the  addition  of  n  c.c. 
of  antitoxin  to  a  given  quantity  of  poison.  The  calcu- 
lated figures  are  obtained  under  the  assumption  that  i  c.c. 
of  the  antitoxin  solution  used  is  equivalent  to  4.8  times  the 
used  quantity  of  lysin.  The  constant  of  equilibrium  is 
^=0.13  at  20°  C,  very  nearly  like  that  for  tetanolysin. 
TOXICITY  (q)  OF  STREPTOLYSIN  AFTER  ADDITION  OF  n  c.c.  OF  ITS  ANTILYSIN 


n 

«i 

?obs. 

?calc. 

0 

0 

100 

ICO 

0.025 

0.  12 

88.7 

88.2 

0.05 

0.24 

76.1 

76.9 

0.075 

0.36 

64.8 

66.3 

O.I 

0.48 

55-9 

56.4 

0.125 

0.60 

47-5 

47-5 

O.I5 

0.72 

40.2 

39-8 

0-175 

0.84 

34-6 

33-4 

0.2 

0.96 

28.3 

28.2 

O.225 

1.08 

23-6 

23-6 

0.30 

1.44 

15.0 

15.2 

0.338 

1.62 

"•5 

13-1 

0-375 

i.  80 

8 

II.  2 

°-45 

2.16 

<6 

8.6 

The  observed  figures  are  mean  values  from  three  dif- 
ferent series  of  observations.  The  agreement  between  the 
observed  and  the  calculated  values  is  nearly  perfect  until 
n^  is  about  1.5.  At  high  values  of  n±  the  observed  toxicity 


NEUTRALISATION  OF  H^MOLYSINS  187 

is  somewhat  smaller  than  the  calculated  action.  This  ac- 
cords with  the  observations  on  tetanolysin.  The  experi- 
mental method  was  quite  the  same  in  the  two  cases. 

In  a  lecture  held  before  the  British  Medical  Association 
at  Oxford  in  July,  IQO4,1  Madsen  has  given  curves  repre- 
senting the  toxicity  of  vibrio,  staphylo  and  streptolysin  on 
the  addition  of  increasing  quantities  of  their  specific  anti- 
toxins. These  curves  indicate  clearly  the  fact  that  the 
Ehrlich  phenomenon  is  quite  apparent  in  all  of  them, 
inasmuch  as  the  right  branch  tends  to  bend  asymptoti- 
cally to  the  abscissa. 

In  all  experiments  with  the  lysins  the  temperature, 
which  corresponds  to  the  equilibrium,  is  that  at  which  the 
mixed  fluids,  toxin  and  antitoxin,  are  held  during  I  h.  to 
2  h.  before  the  blood  cells  are  added.  In  this  moment  the 
volume  increases  to  so  high  a  degree  that  the  velocity  of 
reaction  may  be  regarded  as  practically  suspended. 

Cholesterin  displays  a  neutralising  influence  upon  teta- 
nolysin, as  is  seen  from  the  following  table,  indicating  the 
attenuation  of  5  c.c.  of  a  broth  of  tetanus  bacilli  on  the  ad- 
dition of  n  c.c.  of  a  io~6  normal  solution  of  cholesterin  and 
so  much  salt-solution  that  the  total  volume  was  icc.c., 
which  reacted  upon  each  other  during  3  hours  at  37°  C. 
After  this  time  parts  of  this  mixture  were  added  to  8  c.c. 
of  horse  blood  suspension  (2  per  cent),  and  the  action  ob- 
served. The  equation  of  equilibrium  indicates  that  I  mole- 
cule of  reaction-products  results  from  i  molecule  of  lysin, 
and  i  molecule  of  cholesterin.  Of  the  cholesterin-solution 
1.43  c.c.  were  equivalent  to  5  c.c.  of  the  broth,  which  there- 
fore had  the  concentration  2.86  •  io~7  normal. 

1  Madsen:  British  Medical Journal^  Sept.  10,  1904,  p.  12. 


188 


LECTURES   ON  IMMUNITY 


NEUTRALISATION  OF  TETANOLYSIN  BY  nc.c.  io~6  n  CHOLESTERIN 
AT  37°  C.  (MADSEN  AND  WALBUM) 


« 

?obs. 

?calc. 

0 

100 

100 

o-5 

67.5 

66 

o-75 

5' 

49-5 

i 

34-5 

34 

1.2 

27 

23 

I.4 

15 

14 

1.6 

8 

9 

1.8 

5-5 

6.2 

2 

3-4 

4.2 

If   we   choose   a   concentration   in  which  5  c.c.  of  the 
tetanus  broth  are  contained  in  loc.c.  as  the  unit  concen- 
tration, we  find  a  value  0.02*1  for  K  in  the  equation : 
(Cone,  of  tetanolysin)  x  (cone,  of  cholesterin)= 

K  (cone,  of  compound). 

Even  in  this  case  the  observed  values  of  T  for  high  values 
of  n  are  a  little  less  than  the  calculated  ones. 

Even  some  so-called  neutral  substances  exert  an  influ- 
ence upon  the  haemolytic  action  of  tetanolysin.  The  pres- 
ence of  salts  in  large  doses  increases  the  action.  In  this 
case  the  erythrocytes  are  suspended  in  a  physiological 
solution  of  cane  sugar.  If  to  this  so  much  salt  is  added 
that  the  solution  is  0.04  normal,  the  haemolysis  (during  i 
hour  at  37°  C.)  increases  to  about  the  double  value.  A 
o.oi  normal  solution  is  without  appreciable  influence. 
Different  salts  in  the  same  concentration  seem  to  exert  the 
same  influence.  This  influence  is  probably  due  to  an  ac- 
celeration of  the  velocity  of  reaction.  For  this  reason 
solutions  of  lysin  seem  to  be  more  poisonous  in  a  physio- 
logical salt-solution  than  in  one  containing  cane  sugar. 


NEUTRALISATION  OF  PLEMOLYSINS  189 

The  presence  of  protein,  as  egg-albumen  or  normal 
serum,  protects  the  erythrocytes  from  the  attack  of  bases 
and  much  more  still  from  that  of  lysins  of  bacterial  origin. 
Probably  this  action  consists  chiefly  in  a  diminution  of  the 
velocity  of  reaction.  If  great  quantities  of  normal  serum 
are  added,  they  act  as  an  antitoxin. 

In  mixtures  containing  heavy  doses  of  poison  and  of 
antitoxin,  the  velocity  of  reaction  is  very  much  retarded, 
probably  because  of  the  presence  of  large  quantities  of 
protein  which  as  impurities  accompany  the  preparations  of 
poison  and  of  antitoxin. 

The  antitoxic  influence  of  normal  serum  was  first  ob- 
served by  Ehrlich,1  who  employed  horse-serum  against 
tetanolysin.  Neisser  and  Wechsberg  2  found  a  similar  in- 
fluence of  horse-serum  or  human  serum  on  staphylolysin. 
Madsen  and  I3  observed  a  similar  action  of  chicken  egg- 
white  on  tetanolysin ;  still  greater  is  the  influence  of  egg- 
white  from  duck's  eggs,  according  to  P.  T.  Miiller.4 
Marshall  and  Morgenroth5  made  similar  observations  on 
the  action  of  different  sera  on  different  compound  haemo- 
lysins  (cf.  Chapter  VIII).  The  normal  serum  of  the 
horse,  rabbit,  and  man  are  the  most  efficient,  that  of 
pigeons,  mice,  and  geese  less,  while  that  of  sheep  is  nearly 
insensible.  According  to  P.  T.  Miiller,  the  antitoxic  ac- 
tion against  tetanolysin  is  probably  due  to  the  presence  of 
cholesterin  in  the  horse-serum  or  egg-white.  Against  the 
generalisation  of  this  view  it  may  be  pointed  out  that,  ac- 

1  Ehrlich  :   Berl.  Klin.  Wochenschrift^v.  12  (1898). 

2  Neisser  and  Wechsberg:   Zeitschr.f.  Hygeine,  36.  314,  etc.  (1901). 

3  Arrhenius  and  Madsen  :    Festskrift,  III.  37  and  43  (1902). 

*  P.  T.  Miiller:    Centralbl.  /  Bakteriologic,  I.  34.  567  (1903). 

6  Marshall  and  Morgenroth:  Ztitschr.  f.  klin.  Mcdicin,  47.  fasc.  3  and  4. 


ICp  LECTURES  ON   IMMUNITY 

cording  to  Kyes  and  Sachs,  staphylolysin  is  not  acted 
upon  by  cholesterin.1  Madsen  has  even  found  that  other 
constituents,  and  not  the  cholesterin  alone,  protect  erythro- 
cytes  against  tetanolysin  (still  unpublished). 

The  action  of  different  anti-bodies  on  their  correspond- 
ing poisons  is  supposed  to  consist  in  a  simple  neutralisa- 
tion, molecule  for  molecule.  That  the  process  is  followed 
by  another  phenomenon  is  indicated  by  the  circumstance 
that  at  high  concentrations  of  antitoxin,  where  it  is  in 
excess  beyond  the  toxin  present,  the  calculated  values  are 
often  found  to  exceed  remarkably  the  observed  ones.  An- 
other phenomenon  also,  discovered  by  Danysz,2  indicates 
that  an  excess  of  antitoxin  exerts  a  perturbing  influence. 
Danysz  investigated  the  toxicity  of  mixtures  of  ricin  with 
antiricin.  He  observed  that  a  mixture  of  a  parts  of  ricin 
with  b  parts  of  antiricin  is  less  toxic  if  the  two  constituents 
are  mixed  at  once,  than  if  a  fraction  of  a,  say  one-half,  is 
added  to  the  b  parts  of  antitoxin,  and  after  a  time  the  rest 
of  the  toxin  added  to  the  mixture.  The  same  phenomenon 
was  observed  in  diphtheria  poison  by  von  Dungern,  and3 
with  tetanolysin,  staphylolysin,  and  rennet  by  Sachs.4 
On  the  other  hand,  the  cobra  poison  does  not  display  this 
behaviour. 

To  elucidate  this  remarkable  phenomenon,  which  seems 
to  indicate  that  the  same  quantity  of  poison  may  bind  dif- 
ferent quantities  of  antibody,  a  large  number  of  experi- 
ments were  carried  out  on  tetanolysin  by  Madsen,  and  I 


1  Kyes  and  Sachs:    Berl.  klin.  Wochcnschrift,  Nos.  2-4  (1903). 

2  Danysz:  Ann.  de  PlnsL  Pasteur,  1902. 

8  V.  Dungern:  Deutsche  med.  Wochenschrift,  Nos.  8  and  9  (1904). 
*  Sachs  :    Centrtlbl.  /.  Baktcriologic,  37.  Part  II,  251  (1904). 


NEUTRALISATION  OF  H^EMOLYSINS 


IQI 


afterward  calculated  the  results.1  Preliminary  experiments 
showed  that  the  effect  increased  with  the  quantity  of  anti- 
toxin present  and  that  the  dilution  of  the  reacting  sub- 
stances exerted  no  influence,  so  that  the  prevailing  chemical 
process  must  be  a  monomolecular  one. 

One  c.c.  of  a  bouillon  containing  tetanolysin,  was  added  to 
0.8  c.c.  of  a  solution  containing  antilysin  of  which  0.18  c.c. 
were  equivalent  to  I  c.c.  of  the  solution  containing  the  lysin. 
This  mixture  was  kept  at  37°  C.  for  a  certain  time,  /,  and 
afterward  mixed  with  3  c.c.  of  the  poison  and  the  whole 
held  at  37°  C.  during  30  minutes.  The  toxicity,  q,  was  de- 
termined in  the  ordinary  way  and  found  to  increase  with 
the  time,  /,  so  that  q  converged  against  a  maximum  value 
G^.  If  q9  valid  for  the  time  o  is  taken  as  a  unit,  the  dif- 
ference q— qQ  is  a  measure  of  the  effect  investigated.  The 
difference  q^  —  q  indicates  the  progress  of  the  effect  with 
time.  This  quantity  is  treated  as  corresponding  to  a  mono- 
molecular  process  with  the  constant  of  reaction  K.  The 
results  are  given  in  the  following  table  :  — 

THE  PROGRESS  OF  DANYSZ'S  EFFECT  FOR  TETANOLYSIN  WITH  TIME 


t  (hours) 

9 

f-fo 

r,-f 

log  (fa)  —  q  ) 

K 

0 

.00 

0 

0.60 

0.778  — 

— 

0.167 

.04 

0.04 

0.56 

0.748  — 

O.lSo 

0.5 

.14 

0.14 

0.46 

0.663  - 

0.230 

I 

.24 

0.24 

0.36 

0.556- 

O.222 

2 

•33 

o-33 

0.27 

0.431  - 

0.173 

4 

•47 

0.47 

0.13 

O.II4  ~~ 

0.168 

6 

•57 

0-57 

0.03 

0.477  -  2 

0.217 

00 

.60 

0.60 

o 

Mean  0.197 

1  Madsen  and  Arrhenius :  Medd.  fr.  Vet.  —  Ak  :  s.  Nobelinstitut,  1.  No.  3 
(1906). 


192 


LECTURES  ON  IMMUNITY 


In  the  same  manner  TTwas  found  at  19.7°  to  be  0.067 
and  at  27°  C.  to  be  0.105.  This  corresponds  to  an  increase 
of  the  velocity  of  reaction  in  the  proportion  1.86:  i  and 
1.87  :  i  respectively  for  an  elevation  of  the  temperature  of 
10°  C.  This  reaction  belongs,  as  the  constancy  of  K  indi- 
cates, to  the  order  of  monomolecular  reactions. 

In  other  experiments  the  quantity  of  antilysin,  A,  was 
varied,  and  the  following  values  of  q^—q§  were  found. 
The  quantities  of  lysin,  Z,  were  always  the  same,  namely, 
i  c.c.  in  the  first  and  3  c.c.  in  the  second  fraction,  and  the 
experiments  were  otherwise  executed  as  indicated  above. 

THE  MAGNITUDE  OF  THE  EFFECT  OF  DANYSZ  AS  DEPENDENT  UPON  THE 
QUANTITY  OF^  ANTITOXIN  USED 


FIRST  FRACTION 

?oo  -ft 

Observed 

Calculated 

0.2  C.C.  A+\  C.C.Z 

0.05 

0.02      (0.02) 

0.4  c.c.  A  +  I  c.c.  L 

0.23 

0.21       (0.22) 

0.6  c.c.  A  -f  i  c.c.  L 

0-39 

0.40       (0.41) 

0.8  c.c.  A  +  i  c.c.Z 

0.60 

0.60      (0.63) 

1.2  C.C.  A  +  I  C.C.Z 

0.97 

0.99       (0.87) 

The  calculated  values  are  found  under  the  assumption 
that  the  effect  is  proportional  to  the  excess  of  antitoxin  over 
that  (0.18  c.c.)  equivalent  to  the  quantity  of  lysin  (i  c.c.) 
present  in  the  first  fraction.  This  proportionality  is  very 
striking  in  the  figures  above.  The  effect  may  also  be  cal- 
culated as  the  quantity  of  antitoxin  bound  by  the  poison, 
if  the  experiments  are  executed  as  above,  minus  the  cor- 
responding quantity  if  the  total  quantity  of  poison  is  added 
at  once.  The  figures  calculated  in  this  manner  are  written 
in  parentheses. 


NEUTRALISATION   OF   H^EMOLYSINS  193 

Evidently  the  effect  depends  upon  some  slow  molecular 
change  in  the  antitoxin  which  is  not  bound  by  toxin.  This 
process  goes  on  only  in  the  presence  of  the  neutralisation 
products  of  toxin  and  antitoxin  or  of  free  toxin  itself, 
which  therefore  may  be  assumed  to  bind  the  transformed 
antitoxin,  so  that  the  reaction  can  proceed  further.  The 
circumstance  that  the  effect  of  Danysz  is  not  observed 
with  cobra  poison  seems  to  indicate  that  it  is  the  poison 
itself  which  binds  the  transformed  antitoxin.  For  in  this 
special  case  the  neutralisation  is  nearly  complete,  just  as 
the  neutralisation  of  a  strong  acid  with  a  strong  base  ;  and 
therefore,  if  the  antitoxin  is  present  in  excess,  no  sensible 
quantity  of  free  poison  exists  in  the  solution,  and  hence 
we  should  expect  that  the  effect  would  not  be  apparent. 

Because  of  the  inverse  reaction  of  the  reaction-products, 
new  quantities  of  toxin  are  always  free  to  bind  the  trans- 
formed antitoxin.  This  new  reaction  of  (the  modified)  anti- 
toxin and  toxin  is  much  nearer  a  complete  one  than  the 
chief  reaction  between  these  substances  which  prevails 
during  the  first  time  of  reaction,  and  which  therefore 
corresponds  to  the  equilibrium  studied  before.  Conse- 
quently we  find  that  the  bond  between  toxin  and  antitoxin 
"is  strengthened  with  time."  Therefore  also  the  toxicity 
of  solutions  containing  an  excess  of  antitoxin  is  found  to  be 
inferior  to  the  calculated  value.  In  this  way  it  is  explica- 
ble that  mixtures  with  a  very  large  excess  of  antitoxin  may 
be  practically  harmless,  although  the  calculation  does  not 
indicate  it.  This  circumstance  explains  some  experiments 
of  Madsen,  in  which  he  allowed  an  "innocuous"  mixture 
of  diphtheria-toxin  with  antitoxin  (hence  containing  a  very 
great  excess  of  free  antitoxin)  to  diffuse  into  a  gelatinous 


IQ4  LECTURES  ON  IMMUNITY 

solution  over  which  the  mixture  was  placed  in  a  test-tube. 
If  the  mixture  had  been  conserved  for  a  certain  time 
(about  half  an  hour  at  room  temperature)  there  was 
no  indication  that  free  toxin  diffused ;  but  if  the  mixture 
was  used  as  it  was  freshly  prepared,  the  toxin  diffused 
downward,  so  that  the  lower  parts  of  the  solid  gelatinous 
solution  contained  two  lethal  doses  for  guinea-pigs.  Such  a 
strengthening  of  the  chemical  bonds  is  very  often  assumed 
in  the  doctrine  of  immunity,  and  it  corresponds  really  to 
the  phenomenon  of  Danysz. 

Therefore  the  strongly  toxic  solutions  in  which  tetanoly- 
sin  has  been  added  in  fractions  slowly  lose  their  abnormal 
toxicity,  and  after  a  time  (about  6  hours  at  37°  C.) 
they  are  no  more  toxic  than  the  corresponding  mixtures 
which  have  not  been  fractionated. 

The  results  of  the  experiments  of  von  Dungern  regard- 
ing diphtheria-toxin  correspond  in  their  general  features 
with  those  for  tetanolysin,  so  that  there  is  every  reason  to 
believe  that  the  cause  is  identical  in  the  two  cases.  The 
same  may  be  said  of  the  other  cases  in  which  Danysz's 
phenomenon  has  been  observed,  but  the  experimental  data 
are  extremely  meagre. 

Portier  and  Richet  observed  a  peculiar  phenomenon, 
which  at  first  seems  rather  inexplicable,  but  which  is  very 
similar  to  the  phenomenon  of  Danysz,  and  therefore  may 
be  interpreted  in  an  analogous  manner.  They  prepared 
a  solution  of  the  poison  contained  in  the  filaments  of 
ccelenterates  (Actinia  or  Physalis),  which  produces  the 
same  effects  as  the  poison  of  Urtica,  by  macerating  these 
filaments  in  glycerin  and  water.  The  poison  was  injected 
into  the  veins  of  pigeons  or  dogs,  and  caused  a  deep  sleep, 


NEUTRALISATION  OF  H^MOLYSlNS  19$ 

by  virtue  of  which  it  was  called  hypnotoxin.  In  greater 
doses  death  results  under  symptoms  of  asphyxia.  The 
experimenters  hoped  to  produce  an  antitoxin  in  the  usual 
way  by  injecting  increasing  doses  into  the  veins  of  the 
animals.  But  they  did  not  succeed,  because  "  if  an  animal 
receives  in  a  first  injection  a  parts  of  the  poison  and  in  a 
second  injection  b  parts,  it  is  killed  almost  instantaneously 
after  the  second  injection  ;  whereas  an  animal  in  which  the 
dose  a  -f-  b  is  injected  at  once  does  not  show  very  grave 
symptoms  of  intoxication,  from  which  it  soon  recovers."  1 

1  Portier  and   Richet :  Bulletin  du   musee  oceanographique  de  Monaco^ 
25  Dec.,  1905,  p.  10,  No.  56, 


CHAPTER  VII 

NEUTRALISATION  OF  DIPHTHERIA-TOXIN,  RICIN,  SAPO- 
NIN,  AND  SNAKE-VENOMS 

IN  very  nearly  the  same  manner  as  tetanolysin  behaves 
the  practically  most  important  of  all  toxins,  namely,  diph- 
theria-toxin. Through  the  circumstance  of  its  preparation 
and  standardisation  upon  a  large  scale,  a  great  number  of 
experiments  have  been  carried  out  with  it.  Unfortunately 
in  most  of  these  experiments  but  a  few  (4-6)  points  in  the 
neutralisation  curves  have  been  determined,  and  no  indica- 
tions are  given  of  the  magnitude  of  the  experimental  errors. 
This  is,  of  course,  due  to  the  circumstance  that  we  are  still 
in  the  first  beginning  of  the  development  of  the  quantitative 
side  of  this  question.  In  a  memoir  in  the  Centralblatt  fur 
Bakteriologie  (1903),  p.  630  et  seq.,  Madsen  reported  a 
greater  number  of  measurements  of  several  preparations  of 
this  toxin  than  had  been  generally  done.  As  illustration 
may  be  given  the  values  for  poison  No.  471  in  February- 
March,  1902  (5  months  old),  and  in  November  of  the 
same  year  (14  months  old).  The  letters  n  and  q  corre- 
spond, as  for  tetanolysin  above,  to  the  quantity  of  antitoxin 
added  and  toxicity. 

As  will  be  seen  from  these  figures,  the  addition  of  the 
first  quantities  of  antitoxin  seem  not  to  diminish  the  toxicity 
of  the  poison,  the  observed  toxicity  remains  constant,  and  a 
decrease  of  ^obs-  is  not  apparent  until  the  quantities  0.05 
respt.  o.i 8  of  antitoxin  have  been  added.  From  this  Mad- 

196 


NEUTRALISATION  OF  SIMPLE  POISONS 


197 


POISON  471.    FEB.-MARCH,  1902 

POISON  471.    Nov.,  1902 

n 

?obs. 

fcalc. 

n 

$obs. 

fcalc. 

O 

50 

67 

0 

35 

67 

0.05 

5° 

58 

0.06 

35 

56 

O.I 

45 

48 

0.  12 

35 

45 

0.15 

40 

40 

0.18 

35 

36 

0.2 

30 

31 

0.24 

18 

25 

0.25 

20 

23 

o-3 

H 

15 

0-3 

15 

15 

0.36 

8 

8 

0-35 

io—8 

9 

0.4 

7 

5 

0.4 

6 

5 

0.48 

3 

3 

0.45 

3 

3 

0.56 

i 

2 

0.6 

i 

I 

sen  concluded  —  in  agreement  with  Ehrlich  l  —  that  a  frac- 
tion of  the  antitoxin-binding  substance  is  not  poisonous, 
and  that  it  binds  antitoxin  before  the  toxin  itself.  Such  a 
substance  is  called  prototoxoid  by  Ehrlich.  As  the  quan- 
tity, n,  necessary  to  determine  a  decrease  of  the  toxicity 
is  greater  with  the  old  than  with  the  fresh  poison,  the  con- 
clusion was  drawn  that  the  quantity  of  prototoxoid  in- 
creases with  time,  and  perhaps  as  the  preparation  was 
quite  fresh  it  may  at  first  have  contained  no  prototoxoid 
at  all. 

This  was  in  complete  agreement  with  Ehrlich's  ideas, 
but  on  another  point  regarding  the  existence  of  so-called 
toxons  or  epitoxins  Madsen  differed  from  Ehrlich.  As  will 
be  seen  from  the  preceding  table,  the  phenomenon  of  Ehr- 
lich is  very  prominent,  the  same  quantity  of  antitoxin  pro- 
ducing a  much  less  marked  reduction  of  the  toxicity  at  the 
beginning  of  the  neutralisation  than  later  on.  This  is 
explained  by  the  chemical  equilibrium  between  toxin  and 

1  Ehrlich:  Deutsche  med.  Wochenschrift,  No.  38  (1898);  Aug.  31,  Sept.  7 
and  14  (1903). 


198  LECTURES  ON  IMMUNITY 

antitoxin  on  the  one  hand  and  the  products  of  their  reaction 
on  the  other  hand,  as  the  calculated  figures  show.  These 
are  calculated  from  the  equation  valid  for  the  neutralisa- 
tion of  tetanolysin,  only  the  constant  of  equilibrium  here 
is  about  eight  times  lower  than  there ;  in  other  words,  the 
reaction  proceeds  farther  in  the  binding  of  diphtheria- 
toxin  than  in  the  binding  of  tetanolysin. 

When  the  toxicity  sinks  below  one,  the  animals  under 
experiment  do  not  die  after  the  injection  of  the  quantity  of 
poison  employed  (o.  I  c.c.).  By  administering  greater  doses 
it  is  still  possible  to  kill  the  animals.  But  if  the  quantity 
of  antitoxin  exceed  a  certain  amount,  the  animals  are  not 
killed  (in  short  time,  eight,  days),  but  show  other  symptoms 
of  the  disease ;  after  an  incubation  time  of  more  than  a 
week  paralysis  occurs.  Now  Madsen  and  Dreyer l  showed 
that  such  paralysis  is  sometimes  observed  also  after  the 
injection  of  a  quantity  of  pure  diphtheria-poison  less  than 
the  lethal  dose.  The  free  poison  injected  subcutane- 
ously  gives  other  symptoms,  namely,  necrosis  and  alopecia 
at  the  site  of  injection.  Ehrlich  and  his  pupils  now  con- 
tend that  with  mixtures  of  toxin  and  antitoxin  which  do 
not  kill  the  animals  but  produce  paralysis,  the  local 
effects  at  the  site  of  injection  are  much  less  than  after 
the  injection  of  the  corresponding  quantity  of  free  poison, 
whereas  the  paralysis  is  much  stronger  with  the  use  of  the 
mixture  than  with  the  free  poison;  and  therefore  the 
paralytic  result  is  ascribed  to  a  poison,  toxon  or  epitoxin, 
which  remains  after  the  neutralisation  of  the  true  toxin. 
According  to  Madsen  the  difference  observed  depends 
upon  the  following  circumstances.  The  greater  part  of 

1  Dreyer  and  Madsen :   Festskrift,  Copenhagen,  No.  5  (1902). 


NEUTRALISATION  OF  SIMPLE  POISONS  199 

the  free  poison  is  bound  near  the  area  of  injection.  The 
remainder  on  entering  the  circulation  is  therefore  relatively 
harmless.  The  mixture  behaves,  however,  in  a  wholly 
different  manner.  If  the  greater  part  of  its  free  poison 
is  bound  near  the  area  of  injection,  the  diffusing  mixture 
on  entering  the  circulation  gives  off  free  poison  through 
dissociation  of  the  toxin-antitoxin  compound  and  therefore 
causes  a  much  stronger  paralysis  than  does  the  smaller 
quantity  of  originally  free  poison.  It  must  also  be  con- 
ceded that  if,  as  in  the  case  of  poison  No.  471,  in  the  one 
case  less  than  one  lethal  dose,  and  in  the  other  case  about 
forty  lethal  doses,  together  with  a  large  quantity  of  anti- 
toxin, are  injected,  the  animal  will  have  much  more  diffi- 
culty in  freeing  its  body  of  the  poison  in  the  second  than  in 
the  first  case.  For  in  the  first  case  it  has  only  to  neutral- 
ise and  eliminate  less  than  one  lethal  dose  ;  while  in  the  sec-, 
ond  case,  after  the  neutralisation  or  elimination  of  one  lethal 
dose,  new  quantities  of  poison  are  set  free  to  be  eliminated 
from  the  animal's  body.  In  the  meantime  large  enough 
quantities  of  poison  to  cause  a  marked  paralysis  may  diffuse 
to  the  nervous  organs  and  disturb  their  functions.  From  this 
point  of  view  the  long  period  of  incubation  is  also  easily 
understood.  There  is  therefore  no  adequate  ground  to 
assume  the  presence  of  a  poison  such  as  the  toxon  or  epi- 
toxin  of  Ehrlich,  different  from  the  lethal  poison  in  the 
diphtheria  poison.  In  recent  times  a  great  number  of  in- 
vestigations have  been  done  to  strengthen  the  probability 
of  the  existence  of  "toxons."  Morgenroth1  has  made  a 
very  elaborate  study  of  the  action  upon  guinea-pigs  of  pure 
diphtheria-toxin  and  of  mixtures  with  antitoxin.  He  con- 

1  Morgenroth:  Zeitschr.f.  Hygiene,  48.  177  (1904). 


200  LECTURES  ON  IMMUNITY 

trasted  the  difference  between  the  action  of  pure  toxin  and 
of  a  mixture  of  toxin  and  antitoxin,  so  that  there  is  no  doubt 
upon  that  point.  But  there  is  also  no  doubt  that  this  dif- 
ference may  be  as  well  explained  by  the  presence  of  re- 
action-products of  toxin  and  antitoxin  in  the  solution  as  by 
the  assumption  of  a  different  poison  in  the  two  cases. 

There  is  another  experiment  by  van  Calcar,1  which  is 
cited  by  the  many  pupils  of  Ehrlich,  who  attempt  to  defend 
his  views,  v.  Calcar  believed  he  had  found  that  it  was 
possible  by  the  aid  of  diffusion  under  pressure  to  separate 
diphtheria  poison  from  the  accompanying  "toxon";  the 
latter,  he  reported,  was  not  able  to  pass  through  a  membrane 
while  the  real  toxin  diffused.  Romer2  has  repeated  the 
experiment  of  v.  Calcar  and  found  that  it  was  impossible 
to  detect  "  the  least  difference  in  the  behaviour  of  the  origi- 
nal diphtheria  poison  and  of  its  diffusion-products."  Fur- 
thermore, he  subjected  the  results  of  v.  Calcar  to  a  critical 
examination  and  stated  that  his  experiments  did  not  war- 
rant the  conclusion  that  it  is  possible  to  separate  toxons 
from  diphtheria-toxin.  In  the  laboratory  of  Madsen,  Wai- 
bum  has  made  a  thorough  investigation  of  v.  Calcar's 
experiment  and  come  to  the  same  conclusion  as  Romer,  so 
that  there  seems  to  be  no  doubt  that  "toxon"  cannot  be 
separated  from  diphtheria-toxin  by  means  of  diffusion 
under  the  conditions  employed  by  v.  Calcar. 

The  "  prototoxoid "  also  seems  to  be  unproved,  if  we 
subject  the  experimental  material  to  a  closer  analysis. 
On  surveying  the  material  published  by  Madsen,  it  struck 
me  that  it  had  not  been  employed  as  exhaustively  for  the 

1  Van  Calcar:  Berl.  klin.  Wochcnschrift,  No.  39  (1904). 

2  Romer:  Bchrings  Bcitrage  z.  exp.  Thcrapit  (1904). 


NEUTRALISATION  OF  SIMPLE  POISONS 


201 


purposes  of  calculation  as  might  have  been.  A  recalcula- 
tion in  accordance  with  the  rules  valid  in  the  exact  sciences 
(cf.  page  13)  gave  a  neutralisation  curve  which  did  not 
show  the  presence  of  "  prototoxoid  "  in  the  poison  No.  471 
in  the  experiments  of  November,  1902.  I  therefore  made 
a  recalculation  of  all  the  data  relative  to  the  poisons  exam- 
ined by  Madsen.  For  the  poison  No.  471  I  obtained  the 
following  results :  — 


FOR  FEBRUARY,  1902 

NOVEMBER,  1902 

SEPTEMBER,  1903 

• 

?obs. 

?calc. 

n 

?obs. 

?calc. 

n 

?obs. 

?calc. 

0 

100 

100 

O 

100 

100 

0 

IOO 

IOO 

0.05 

744 

87.5 

0.06 

79.3 

86.5 

O.I 

7S-i 

75-1 

O.I 

72.8 

75-i 

0.12 

76.0 

73-2 

0.15 

62.6 

62.7 

0.15 

57.6 

62.7 

0.18 

64.7 

59-8 

0.2 

47.6 

50.6 

O.2 

49.8 

50.6 

0.24 

5°-9 

46.6 

0.25 

45-8 

38.6 

0.25 

32.2 

38-6 

0.3 

39-1 

34-0 

o-3 

25-9 

27-3 

0-3 

28.0 

27-3 

0.36 

23.1 

22.4 

0.35 

17-3 

17-5 

0.35 

17.2 

17-5 

0.4 

14.8 

iS-7 

0.4 

9-6 

9.9 

0.4 

ii.  i 

9-9 

0.48 

8.3 

7.0 

0.45 

5-3 

6.0 

0.45 

5.6 

6.0 

0.54 

2-5 

4-5 

0.5 

3-' 

4.1 

o-5 

1.2 

4.1 

0.6 

2.6 

3-o 

0.6 

1.6 

2.6 

Abs.  toxicity  =  4.1 

Abs.  toxicity  =  2.86 

Abs.  toxicity  =  2.14 

The  constant  of  equilibrium  remained  unchanged 
(  =  0.012),  in  the  whole  time.  No  traces  of  prototoxoids 
may  be  detected  from  the  new  calculation.  This  is  also 
the  case  for  two  other  poisons,  A  and  C,  examined  previ- 
ously by  Madsen,  and  in  which  he  supposed  large  quan- 
tities of  prototoxoid  to  be  present.  If  prototoxoid  had 
been  present  in  the  poison  No.  471,  it  would  have  been 
most  evident  in  the  later  researches  (of  September,  1903), 
since  it  was  then  rather  old.  But  just  in  this  case  the 


202  LECTURES  ON  IMMUNITY 

agreement  between  observation  and  the  calculation  by 
which  no  prototoxoid  is  supposed  to  exist,  is  very  good 
for  low  values  of  n.  The  hypothesis  of  prototoxoids 
seems  therefore  untenable.  But  on  the  other  hand,  the 
poisonous  effects  of  No.  471  had  fallen  very  remarkably 
in  the  seventeen  months  —  to  very  nearly  half  the  original 
toxicity  —  without  change  in  the  antitoxin-binding  property 
of  the  poison.  For  this  same  reason  Ehrlich  supposed  that 
the  poison  is  slowly  converted  into  an  innocuous  or  less 
poisonous  substance  with  the  same  antitoxin-binding  prop- 
erties as  the  toxin  itself  (cf .  p.  1 84).  This  new  substance 
is  called  syntoxoid  by  Ehrlich. 

The  several  preparations  of  diphtheria-toxin  differ 
from  each  other  in  showmg  rather  marked  differences 
in  their  constants  of  equilibrium:  No.  471,  JT=o.oi2; 
poison  A,  ^=0.03;  poison  C,  K=  0.004.  It  will  be  nec- 
essary to  make  new  experiments  on  this  interesting  ques- 
tion (and  similar  ones  for  tetanolysin)  before  this  can  be 
elucidated.  The  observed  peculiarity,  that  K  has  rather 
different  values,  might  be  explained  by  supposing  that  the 
poison  is  loosely  combined  with  or  absorbed  by  some 
concomitant  substance,  for  instance  by  albuminous  sub- 
stances contained  in  the  preparations,  and  that  therefore 
only  a  certain  fraction  of  the  toxin  enters  into  the  equi- 
librium with  antitoxin.  This  fraction  is  different  in  differ- 
ent preparations  of  the  diphtheria  poison,  according  to 
their  different  content  of  the  reacting  proteins,  and  the 
less  this  fraction  the  greater  would  be  the  constant  of 
the  equilibrium.  This  view  is  supported  by  the  observa- 
tion of  Madsen  that  the  value  of  K  for  another  poison, 
namely  crotalus  venom,  is  different  when  injected  into 


NEUTRALISATION  OF  SIMPLE    POISONS  203 

rabbits  than  with  guinea-pigs.1  But  perhaps  this  differ- 
ence depends  only  upon  the  different  mode  of  injection 
(intra-venous  respectively  intra-peritoneal). 

In  the  same  manner  behaves,  according  to  the  researches 
of  Madsen  and  Walbum,2  ricin  and  its  antibody,  at  least 
in  so  far  as  the  agglutinating  action  of  ricin  on  red 
blood-corpuscles  (of  rabbits)  is  concerned.  The  agglu- 
tinating power  of  the  ricin  was  measured  by  observing 
the  limpidity  of  5  c.c.  of  a  one  per  cent  suspension  of  red 
blood-corpuscles  added  to  2  c.c.  of  the  solution  and  there- 
after held  at  37°  C.  for  20  minutes.  As  example  may  serve 
the  following  figures  :  — 

n  =o  0.025  0.035  °-°45  o-°55  0.065  °-°75  0.087  o-1 
?obs.  =6.7  6.7  3.6  2.1  1.5  1.0  0.8  0.64  <o.5 
?caic.  =  (i9'7)  6-8  3-6  2-1  M  1.0  0.8  0.63  0.12 

One  c.c.  of  the  antiricin,  prepared  by  injection  into  a 
goat,  was  equivalent  to  29  c.c.  of  the  solution  of  ricin  em- 
ployed (containing  i  per  cent  of  a  ricin  preparation  from 
Merck).  The  constant  of  equilibrium  was  ^=0.0537.  The 
formula  was  the  same  as  that  used  for  tetanolysin. 

As  is  evident  from  these  figures,  the  prototoxoid  phe- 
nomenon is  very  marked.  No  sensible  neutralisation  takes 
place  until  about  0.75  equivalents  of  antitoxin  have  been 
added.  But  this  phenomenon  was  "very  inconstant,  and 
was  observed  in  only  half  the  number  of  the  cases  exam- 
ined." The  authors  could  not  determine  what  accidental 
circumstances  could  have  caused  this  contradictory  be- 
haviour of  ricin ;  the  so-called  prototoxoid  effect  was 

1  British  Medical  Journal,  Sept.  10,  1904,  p.  14. 

2 Madsen  and  Walbum:    Centralbl.  f.  Bakteriologic,  Abt.  I.,  36.  242  (1904). 


204  LECTURES  ON  IMMUNITY 

observed  in  some  experiments,  whereas  other  experiments 
executed  with  the  same  preparations  and  on  the  same  day 
(with  the  same  horse  blood)  did  not  indicate  the  presence 
of  a  prototoxoid. 

As  illustration  of  ricin  which  does  not  show  the 
"protoxoid"  zone,  the  following  figures  of  Madsen  and 
Walbum l  may  suffice :  — 

n      =o  o.i         0.2        0.3        0.4          0.5  0.6  0.7          0.8 

?obs.  =100  88  73  63  44  27.3  15.9  11.9  7.1 
?caic.  =100  86  72  58  44  31.3  19.4  1 1.0  6.4 

Here  the  constant  of  equilibrium  is  only  0.014.  Madsen 
and  Walbum  found  that  the  strength  of  the  antiricin  de- 
creased continually,  sinkiiig  from  the  value  I  to  0.4  in 
47  days  and  to  0.196  in  42  additional  days,  which  corre- 
sponds closely  to  a  monomolecular  reaction  (cf.  p.  37  ff.). 
During  the  same  time  the  constant  of  equilibrium  dimin- 
ished in  the  proportion  0.537  :  0.0142. 

The  ricin  has  another  toxic  effect.  On  subcutaneous 
injection  it  kills  guinea-pigs,  even  if  it  is  used  in  very 
minute  amount.  Madsen  and  Walbum  determined  the 
lethal  dose  to  be  0.000123  g.  The  toxicity  is  therefore 
expressed  by  the  inverse  number,  8130.  Madsen  and 
Walbum  took  a  quantity  of  poison  200  times  less  (40.7) 
or  0.005  g.  They  added  different  quantities  of  anti- 
ricin—  between  o.oi  and  0.035  c-c* — t°  this  quantity  of 
ricin,  held  the  mixture  for  20  minutes  at  37°  C.  and  injected 
it  thereafter  into  guinea-pigs.  They  found  that  the  dif- 
ferent mixtures  contained  the  following  number  of  lethal 
doses : — 

1  Madsen :  British  Medical  Journal,  Sept.  10, 1904,  p.  9. 


NEUTRALISATION  OF  SIMPLE  POISONS  205 

TOXICITY  OF  MIXTURES  OF  THE  NERVOUS  POISON  IN  RICIN  AND  ANTIRICIN 


«=c.c. 

fobs. 

?calc. 

0 

40.7 

40.7 

0.01 

25 

25.6 

0.0125 

21 

22 

0.015 

'7 

18.6 

0.02 

12 

12.2 

0.0225 

9 

9-5 

0.025 

7 

7 

0.0275 

5 

5 

0.03 

4 

3.5 

0.0325 

3 

2.7 

0-035 

2 

I 

The  values  used  are/ =  40,  that  is,  0.025  c.c.  of  the  anti- 
ricin  is  equivalent  to  0.005  g.  of  the  ricin.  K  was  found 
to  be  0.00149  and  the  formula  used  was:  — 

[(Cone,  of  free  ricin)  (cone,  of  free  antiricin)  = 

K  (Cone,  of  bound  ricin)*.] 

The  calculated  values  agree  very  well  with  the  observed 
ones.  The  equation  indicates  that  of  two  molecules  of  ricin 
and  two  molecules  of  antiricin  are  formed  three  molecules 
of  innocuous  substance. 

Therefore  we  must  suppose  that  it  is  probably  some  other 
poison  in  the  ricin  preparations  that  causes  the  death  of  ani- 
mals than  that  which  agglutinates  the  red  blood-corpuscles. 
Therefore  the  assertion  of  Ehrlich  that  the  action  of  ricin 
in  vitro  is  of  the  same  order  as  in  the  living  animal,1  can- 
not endure  a  quantitative  examination.  That  these  two 
poisons  are  not  identical  is  known,  but  it  was  possible  that 
they  were  always  present  in  a  given  proportion.  That  this 
is  not  the  case  is  seen  from  Bashford's  experience,  which 

1  Ehrlich:  Fortschrittc  der  Medicin,  No.  2  (1897). 


206 


LECTURES  ON   IMMUNITY 


shows  that  normal  rabbit-serum  interferes  with  the  agglutin- 
ating, but  not  with  the  neurotoxic  action  of  ricin.1 

In  the  same  manner  as  the  nerve-poison  of  the  ricin 
behaves  the  haemolytic  poison  saponin,  according  to  an 
investigation  of  Madsen  and  Noguchi.2  They  investigated 
its  influence  upon  different  quantities  of  blood-corpuscles. 
The  experiments  were  executed  in  the  manner  commonly 
employed,  so  that  to  a  given  quantity  (2  c.c.  of  a  2  per  cent 
solution)  of  poison  (saponin)  a  certain  quantity  of  antitoxin 
(cholesterin)  and  so  much  physiological  salt-solution  was 
added  that  the  total  quantity  was  4  c.c. 

NEUTRALISATION  OF  0.04  G.  SAPONIN  BY  MEANS  OF  n  c.c.  OF 
o.  i  n  CHOLESTERIN 


N. 

BLOOD  EMULSION  OF 

TOXICITY 

(mean) 

TOXICITY 
(calc.) 

i.*5  % 

2-5% 

5% 

0 

100 

100 

100 

IOO 

95-2 

0.01 

79-5 

82.4 

79-3 

80.4 

78.5 

0.015 

67.5 

71.0 

71.8 

7O.I 

71-5 

O.O2 

54-6 

57.6 

62.1 

58.1 

62.9 

O.O25 

48.1 

53-i 

56 

52.4 

55-6 

0.03 

44 

45-4 

48.3 

45-9 

48.3 

0.04 

34-5 

4i 

40.6 

38.7 

35-4 

0.05 

26.7 

33-4 

29-3 

29.8 

24.4 

O.O6 

17.7 

21.2 

18.1 

19  o 

15-7 

O.O/ 

n.  i 

12.8 

9-4 

ii.  i 

9.8 

0.08 

7.8 

6.7 

4-3 

6-3 

6.1 

O.I 

3-7 

3-2 

2.4 

3-i 

2.8 

0.12 

P-7 

1-4 

1.2 

1.4 

1.4 

0.14 

0.67 

0.62 

0.51 

0.6 

0.8 

o.  16 

0.34 

o-43 

0.42 

0.4 

o-5 

Of  the  cholesterin  solution  0.053  c.c.  is  equivalent  to  0.04  g. 
of  saponin,  or  i  c.c.  to  0.76  g.     K  is  given  as  K=  0.0166. 

1  Bashford:  Journal  of  Hygiene,  4.  56  (1904). 

2  Madsen  and  Noguchi :    Oversigt  over  d.  k.  danskc  Vid-Sehtts  Forh.y  No.  6, 
457  (1904). 


NEUTRALISATION  OF  SIMPLE  POISONS  2O/ 

According  to  this  the  molecular  weight  of  saponin  would  be 
7600,  if  i  gramme-molecule  of  cholesterin  (C27H46O  =  386) 
is  supposed  to  be  equal  to  a  gramme  equivalent,  and  the 
same  is  valid  for  the  saponin,  supposed  to  be  pure. 

The  different  blood  suspensions  (from  horse  blood),  the 
concentration  of  which  varies  in  the  proportion  i  :  4,  give 
within  the  experimental  errors  the  same  value  for  the 
toxicity.  This  circumstance  seems  to  indicate  that  the 
absorption  of  a  part  of  the  poison  in  the  erythrocytes  does 
not  disturb  the  equilibrium.  This  depends  probably  upon 
the  circumstance  that  the  quantity  of  poison  absorbed  by 
the  erythrocytes  is  insignificant  compared  with  that  in  the 
surrounding  medium.  The  saponin-cholesterin  reaction 
was  selected  for  this  special  investigation  because  its 
velocity  of  reaction  is  so  high  that  it  cannot  be  measured 
with  the  methods  now  used.  The  mixtures  of  saponin 
(in  2  per  cent  aqueous  solution)  and  of  cholesterin  (in 
o.i  n.  =  3.86  per  cent  ethereous  solution)  were  mixed,  and 
held  at  37°  C.  for  three  hours.  The  ether  which  did  not 
evaporate  in  this  time  was  removed  in  vacuo,  after  which 
so  much  salt-solution  was  added  that  the  quantity  of  saponin 
in  the  solution  was  i  per  cent.  Then  the  quantities  of 
these  mixtures  to  be  investigated  were  placed  in  test-tubes 
and  so  much  salt-solution  was  added  that  the  volume  was 
2  c.c.,  whereafter  8  c.c.  of  the  blood  suspensions  were 
rapidly  poured  into  the  test-tubes  and  mixed  by  shaking. 
The  test-tubes  were  then  placed  in  an  incubator  at  37°  C. 
for  three  hours,  and  then  put  on  ice  and  examined  the  next 
day  in  the  usual  manner. 

There  was  therefore  an  adequate  time  for  the  equilibrium 
to  be  established  after  the  addition  of  the  blood  suspension, 


208 


LECTURES  ON   IMMUNITY 


so  that  we  might  in  this  case  have  expected  that  if  the 
presence  of  the  erythrocytes  has  a  perturbing  influence, 
this  should  be  very  manifest  in  the  present  case,  in  which 
the  quantity  of  erythrocytes  was  in  one  case  double  that 
used  in  such  experiments  in  general. 

But  no  such  influence  is  seen  in  the  figures  of  the  last 
table,  so  that  we  may  on  this  ground  well  conclude  that 
the  perturbing  influence  caused  by  the  solubility  of  the 
poison  in  the  erythrocytes  may  be  neglected  in  these  and 
similar  experiments. 

Some  experiments  with  normal  serum  of  horse  or  ox 
gave  the  same  result,  as  may  be  seen  from  the  following 
table,  in  which  the  calculated  values  are  found  under  the 
assumption  that  i  c.c.  of  normal  ox-serum  is  equivalent  to 
0.006  g.  of  saponin. 

NEUTRALISATION  OF  0.002  G.  SAPONIN  WITH  n  c.c.  OF  NORMAL  SERUM  OF 

Ox  BLOOD 


n 

<W 

^calc. 

O 

100 

100 

O.I 

80.5 

79-4 

0.15 

70.6 

71.7 

0.2 

62.8 

64.5 

0-3 

52.1 

52.2 

04 

444 

42.5 

0-5 

35-3 

344 

0.6 

28.3 

27.9 

0.8 

18.6 

1  8.6 

I.O 

10.7 

13.2 

K-  0.093. 

The  equation  used  for  the  calculation  is  the  same  as  in  the 
last  case. 

Madsen    and    Noguchi    have   made    an    investigation l 

1  Madsen  and  Noguchi :  Oversigt,  1906,  No.  4,  p.  233. 


NEUTRALISATION  OF  SIMPLE   POISONS 


209 


of  the  neutralisation  of  different  snake-poisons  by  their 
antibodies.  These  are  specific,  i.e.  they  do  not  react 
except  with  the  particular  poison  that  was  used  in  the 
injection.  The  cobra-antitoxin  was  secured  from  horse 
blood,  the  two  others  from  goat  blood.  The  snake- 
venoms  contain  different  poisons,  of  which  some  are 
haemolytic,  others  react  chiefly  upon  the  nervous  system 
and  are  lethal  for  animals.  The  antibodies  neutralise  the 
lysins  as  well  as  the  other  poisons. 

In  the  process  of  neutralisation,  the  lysins  of  the  snake 
venoms  behave  rather  like  strong  bases,  the  constant  of 
equilibrium  being  nearly  zero.  This  agrees  well  with  the 
results  of  the  older  experiments  of  Kyes. 

The  following  tables  give  the  details.  The  poisons  and 
their  antibodies  were  allowed  to  react  during  three  hours 
at  37°  C.,  the  total  volume  being  always  the  same  for  the 
same  poison.  After  the  reaction  they  were  mixed  with 
8  c.c.  of  blood  suspension. 

NEUTRALISATION  OF  i  c.c.  OF  0.05  PER  CENT  CROTALOLYSIN  BY  MEANS  OF 
n  c.c.  OF  ANTIVENIN  (5  PER  CENT  DOG  BLOOD) 


n 

?obs. 

?calc. 

0 

100 

100 

0.05 

89 

91 

O.I 

77 

81 

O.I5 

7* 

72 

0.2 

64 

63 

0.25 

54 

53 

o-3 

46 

44 

0-35 

36 

35 

0.4 

24 

26 

0-45 

16 

16 

°-5 

6-3 

7 

o-55 

i-5 

o 

2IO 


LECTURES  ON  IMMUNITY 


The  last  figure  indicates  that  the  quantity  of  free  poison 
exceeds  the  calculated  one,  under  the  assumption  that 
K=  o,  and  that  hence  K  has  a  finite  value.  If  we  calculate 
K  from  this,  placing  I  c.c.  of  antivenin  as  equivalent  to 
1.86  c.c.  of  the  lysin,  we  find  K—  0.0006,  using  the  same 
equation  as  for  tetanolysin.  In  the  experiments  with 
cobralysin  to  each  1000  c.c.  of  horse-blood  suspension  were 
added  8  c.c.  of  o.oi  n.  lecithin.1 

NEUTRALISATION  OF  ic.c.  OFO.I  PER  CENT  COBRALYSIN  BY  MEANS 
OF  wc.c.  OF  ANTIVENIN  (i  PER  CENT  HORSE  BLOOD) 


n 

?obs. 

^calc. 

O 

100 

ICO 

O.I 

1   84 

83 

0.15 

71 

75 

0.2 

65 

66 

0.25 

56 

58 

0-3 

44 

5° 

0.4 

33 

33 

0.5 

16 

16 

0.6 

3-3 

o 

Here  i  c.c.  of  the  antivenin-solution  is  equivalent 
to  1.68  c.c.  of  the  poison.  The  last  observation  gives 
^=0.0016. 

1  Cf.  Kyes  :  Berl.  klin.  Wochenschrift,  No.  19  (1904).  Kyes  finds  the 
following  values  for  cobralysin :  — 


n 

*ObB. 

*calc. 

0 

100 

100 

o-75 

66.7 

66.7 

i-5 

33.3 

33.3 

2.25 

O.I 

0 

Even  here  we  find  a  deviation  from  the  calculated  value  in  the  direction 
that  a  mixture  which  was  calculated  to  be  neutral  showed  haemolytic  proper- 
ties. 


NEUTRALISATION   OF  SIMPLE   POISONS 


211 


NEUTRALISATION  OF  i  c.c.  OF  LYSIN  FROM  ANCISTRODON  PISCIVORUS, 
ACTING  ON  AN  EMULSION  OF  5  PER  CENT  DOG  BLOOD 


n 

?obs. 

*calc. 

0 

100 

100 

O.O5 

93 

94 

O.I 

87 

88 

0.15 

82 

82 

0.3 

77 

76 

0.25 

70 

70 

0-3 

63 

64 

0.4 

53 

52 

o-5 

42 

40 

0.6 

26 

28 

0.7 

17 

16 

0.8 

n 

4 

i 

2 

0 

Here  the  deviation  from  the  calculated  figures  is  still 
greater  than  in  the  two  preceding  cases.  K  is  about 
0.006,  or  a  little  larger  than  for  the  diphtheria-poison, 
which  exhibits  the  least  value  of  K(K=  0.004).  From 
these  experiments  it  follows  that  the  assertion  of  Kyes 
and  Sachs,  that  the  neutralisation  curve  for  cobralysin  is 
quite  rectilinear  (corresponding  to  l£=o),  is  not  exact. 
This  assertion  does  not  even  agree  with  the  experiments 
of  Kyes  himself.  The  conclusions  which  these  authors 
have  drawn  from  their  not  entirely  strict  observations 
can  be  no  longer  maintained.  Even  had  the  curve  been 
quite  rectilinear,  that  would  not  have  allowed  them  to 
conclude  that  a  deviation  from  the  straight  line  indicates 
the  presence  of  toxoids  and  toxons  (cf.  behaviour  of  am- 
monia). It  is  also  noteworthy  that  Kyes  has  made  no 
experiments  with  mixtures  containing  an  excess  of  antily- 
sin,  or  at  least  he  has  not  mentioned  them. 


212 


LECTURES  ON  IMMUNITY 


Regarding  the  nerve-poisons  of  the  venoms,  experiments 
may  be  cited  in  which  the  poisons  were  injected  intra- 
peritoneally  into  guinea-pigs.  The  observations  and  calcu- 
lations were  carried  out  as  in  the  case  of  diphtheria-poison. 
The  following  values  were  obtained  :  — 

NEUTRALISATION  OF  0.006  G.  OF  CROTALUS-POISON  BY  MEANS  OF 
».  c.c.  OF  ANTIVENIN 


n 

<W 

*calc. 

0 

100 

100 

0.25 

75 

75 

o-5 

58 

54 

0.75 

38 

43 

1.0 

29 

31 

1.25 

.  21 

21 

i-5 

H 

'5 

i-7S 

12 

10 

2.O 

8 

7 

2.25 

4 

4 

Here  I  c.c.  of  antitoxin  is  equivalent  to  the  0.006  g. 
of  crotalus-poison.  The  equation  of  equilibrium  indicates 
that  three  molecules  of  reaction-products  are  formed  from 
two  molecules  of  toxin  and  two  of  antitoxin.  The  con- 
stant is  K  =  0.048. 

The  cobra-poison  was  studied  in  the  same  manner.  It 
gave  the  following  figures,  which  are,  however,  too  few  to 
be  used  for  calculation,  but  still  indicate  that  the  poison 
behaves  like  the  crotalus-poison. 

n  =o       I       2       34  c.c.  antitoxin  on  0.003  £•  °f  poison. 

q  (obs.)  =  100     64    36     14    9 

Very  peculiar  results  were  obtained  in  experiments  on 
the  neutralisation  of  the  poison  of  the  water-moccasin 
(Ancistrodon piscivorus).  There  the  toxicity  fell  to  a  mini- 


NEUTRALISATION   OF  SIMPLE   POISONS 


213 


mum  and  then  subsequently  rose,  as  the  following  figures 
indicate :  — 

NEUTRALISATION  OF  WATER- MOCCASIN  POISON  (0.012  G.)  WITH  n.  c.c. 

ANTITOXIN 


n 

*obB. 

n 

«W 

0 

IOO 

8 

19 

2 

56 

9 

24(?) 

4 

44 

10 

19 

5 

33 

20 

36 

6 

24 

40 

65 

The  measurements  seem  to  indicate  that  the  antitoxin 
itself  injured  the  guinea-pigs,  in  whom  it  was  injected  in 
rather  large  quantities  (10  c.c.  in  the  last  experiments). 
The  results  recall  those  obtained  in  the  neutralisation  of 
a  base  with  an  acid  (cf.  p.  173).  The  great  loss  of 
antitoxin  prevented  the  experiments  from  being  carried 
further. 

As  will  be  seen  in  the  next  chapter,  cobra-poison  unites 
with  lecithin  to  form  a  compound,  cobra-lecithid,  of  a  very 
high  haemolytic  action.  Kyes 1  has  isolated  this  cobra- 
lecithid  and  thereafter  prepared  an  antitoxin  against  it  by 
injections  of  this  poison  into  the  veins  of  a  rabbit.  As 
normal  serum  of  rabbit  is  itself  a  little  antitoxic  to  cobra- 
lecithid,  but  loses  this  property  after  heating  for  30 
minutes  to  64°  C.,  the  immune-serum  was  heated  during 
30  minutes  to  64°  C.,  in  which  treatment  the  specific  anti- 
toxin remains  unaltered.  With  these  substances,  cobra- 
lecithid  and  its  antitoxin,  Kyes  did  some  experiments  on 

iKyes:  I.e.,  p.  8. 


214 


LECTURES  ON  IMMUNITY 


ox  erythrocytes,  the   results  of   which  are  given  in  the 
following  table :  — 

NEUTRALISATION  OF  0.4  c.c.  SOLUTION  OF  COBRA-LECITHID  WITH  n  c.c.  OF  ITS 

ANTITOXIN 


« 

«i 

?obs. 

?calc. 

0 

o 

100 

100 

I 

0.4 

65.7 

64.8 

2 

0.8 

39-2 

4I.I 

3 

1.2 

28.2 

27.6 

4 

1.6 

21.2 

20.0 

^=0.25 

The  calculated  figures,  which  agree  very  satisfactorily 
with  the  observed  ones,  were  obtained  by  means  of  the 
equation  found  for  the  neutralisation  of  tetanolysin.  The 
high  value  of  the  constant  shows  that  the  combination  is 
far  from  complete ;  in  other  words  the  neutralisation  curve 
differs  widely  from  a  straight  line. 

Kyes  and  Sachs1  stated  that  cholesterin  has  a  strong 
neutralising  influence  on  cobra-lecithid  as  well  as  on  cobra- 
lysin.  This  action  of  cholesterin  is  even  manifested  against 
the  haemolytic  power  of  tetanolysin  and  olive  oil,  but  not 
against  that  of  staphylolysin  or  arachnolysin. 

Morgenroth2  describes  an  experiment  carried  out  by  him 
with  a  mixture  of  cobralysin  containing  a  little  more  than 
the  double  equivalent  quantity  of  antivenin,  in  the  presence 
of  lecithin.  This  mixture  (in  10  c.c.  of  physiological  salt- 
solution)  was  brought  into  contact  with  rabbit  erythrocytes 

1  Kyes  and  Sachs:  Berl.  klin.  Wochenschrift,  Nos.  2-4  (1903). 

2  Morgenroth :    "  Arbeiten   aus    dem  pathologischen  Institut  zu  Berlin," 
1906,  p.  II.     Cf.  the  experiments  of  Madsen  and  Walbum  with  ricin,  against 
which  Morgenroth  uses  as  an  argument  his  experiment  cited  above. 


NEUTRALISATION  OF  SIMPLE  POISONS  215 

for  3  hours  at  37°  C.  and  thereafter  the  fluid  separated 
from  the  erythrocytes  by  centrifugalisation  and  its  content 
of  cobra-poison  determined.  As  is  so  common,  no  indica- 
tion is  given  of  the  magnitude  of  the  experimental  error, 
which  we  may  estimate  as  very  low,  5  per  cent.  Morgen- 
roth  found  that  "  absolutely  "  (!)  no  cobra-poison  had  been 
absorbed  by  the  erythrocytes.  The  correct  conclusion 
would  evidently  have  been  that  less  than  5  per  cent  of  the 
poison  was  removed.  A  calculation  from  the  figures  given 
above  (K  =0.00 1 4)  shows  that  about  o.i  per  cent  of  the 
poison  was  free  in  the  liquid.  If  now  the  erythrocytes 
had  absorbed  ten  times  this  quantity,  it  would  have  been 
five  times  less  than  the  least  quantity  which  Morgenroth 
would  have  been  able  to  detect.  Perhaps  the  erythrocytes 
absorbed  even  the  antitoxin  in  this  case. 

It  is  to  be  regretted  that  Morgenroth  has  chosen  this 
particular  compound  to  determine  whether  a  partial  dis- 
sociation occurs,  since  it  was  well  known  from  Kyes'  ex- 
periments that  it  is  dissociated  to  an  extremely  low  degree 
(Kyes  asserted  that  it  was  not  dissociated  at  all) ;  and  also 
that  Morgenroth  used  such  a  large  excess  of  antitoxin  to 
still  more  suppress  the  insignificant  degree  of  dissociation. 
Morgenroth  might  well  have  used  much  more  dissociated 
compounds  in  his  experiments  without  still  being  able  to 
detect  the  dissociation-products  with  the  means  employed 
by  him  in  this  case. 

Biltz1  has  investigated  the  neutralisation  of  arsenious 
acid  (As2O3)  by  means  of  "freshly  precipitated  ferric 
hydrate."  This  hydrate  has  a  physical  constitution  like 
that  of  gel,  and  behaves  just  as  a  colloid  in  its  absorption 

1  Biltz:  Ber.  d.  deutschen  chem.  Ges.  37.  3138  (1904). 


2l6  LECTURES  ON   IMMUNITY 

power.  Biltz  finds  that  on  adding  increasing  quantities  of 
arsenious  acid  to  a  given  quantity  (200  c.c.)  of  water  in 
which  are  suspended  10  c.c.  of  the  hydrate,  the  quantity 
absorbed  increases  much  more  slowly  than  the  concentra- 
tion of  the  liquid.  The  increase  of  the  arsenious  acid  ab- 
sorbed by  the  hydrate  is  only  proportional  to  the  fifth  root 
of  the  concentration  of  the  liquid.  This  observation  is  in 
good  concordance  with  other  experiments  on  analogous 
subjects  (for  absorption  by  means  of  charcoal  Schmidt 
found  the  fourth  root,  which  seems  to  be  the  most  general 
case  in  so-called  adsorption  processes). 

Biltz  finds  that  there  is  a  very  close  analogy  between 
this  phenomenon  and  the  neutralisation  of  toxins  by  means 
of  antitoxins.  It  is  very  astonishing  that  Biltz  has  not 
tested  his  idea  on  a  practical  example,  for  instance  on  the 
observations  regarding  the  neutralisation  of  tetanolysin  or 
diphtheria-toxin  published  at  that  time.  If  I  have  under- 
stood Biltz  aright,  the  toxin  would  be  analogous  to  the 
arsenious  acid  in  true  solution  and  the  antitoxin  would  be 
in  the  colloidal  state  and  correspond  to  the  ferric  hydrate. 

From  this  point  of  view  I  have  examined  the  observed 
figures  cited  above  regarding  diphtheria-poison,  tetanolysin 
with  antilysin  or  cholesterin,  and  saponin  with  cholesterin 
or  ox-serum.  In  the  two  first  cases,  where  the  reaction- 
products  enter  into  the  equation  of  equilibrium  to  the 
second  power,  the  formula  of  Biltz  — 

Cone,  of  free  poison  =  A^(conc.  of  poison  in  the  antitoxin )*, 

gives  a  value  of  /  which  rapidly  sinks  with  increasing 
concentration  of  the  antitoxin.  For  the  tetanolysin  with 
antilysin,  /  sinks  from  the  value  4.5  through  the  values 


NEUTRALISATION  OF  SIMPLE  POISONS  2I/ 

2,  3,  and  1.8  and  reaches  at  the  end  the  value  1.3. 
For  the  diphtheria-poison  No.  471  (September,  1903),  the 
corresponding  values  are  150,  n,  7.3  and  4.3.  For  the 
neutralisation  of  tetanolysin  with  cholesterin,  /  sinks 
from  an  infinite  value  through  11.5  to  5.1.  For  the  neu- 
tralisation of  saponin,/  goes  through  a  minimum.  With 
cholesterin  it  gives  for  /-values,  6.5,  3.1,  and  5  ;  with  ox- 
serum  the  values  5,  1.2,  2.8,  and  4.1.  There  can  therefore 
be  no  possibility  that  /  may  be  regarded  as  a  constant, 
and  therefore  the  hypothesis  of  Biltz  must  be  regarded  as 
untenable. 

On  the  other  hand,  we  may  sum  it  up  as  our  experience, 
that  we  are  entitled  to  regard  the  formula  of  Guldberg 
and  Waage,  — 
(Cone,  of  toxin)  x  (cone,  of  antitoxin) 

=  K  (cone,  of  reaction-products)*7, 

where  /=  2  or  1.5,  or  sometimes  i,  as  valid  in  all  the  ex- 
amined cases  of  neutralisation  of  poisons  by  antitoxins. 


CHAPTER  VIII 
THE   COMPOUND   H^MOLYSINS 

SINCE  the  earliest  times  the  injection  of  the  blood  of  ani- 
mals into  the  veins  of  the  human  sick  has  been  practised 
for  therapeutic  purposes.  It  was  always  known  that  these 
experiments  with  "  transfusion "  of  blood  were  dan- 
gerous, and  it  was  later  determined  that  the  serum  from 
animals  exerts  a  "  globulicidal "  action  on  the  erythrocytes 
of  human  origin.  Only  the  blood  of  the  same  species 
(isoserum)  is  innocuous.1 

The  normal  serum  of  an  animal  contains  a  substance 
which  haemolyses  the  erythrocytes  of  animals  of  other 
species,  and  this  substance  was  called  alexin  (protecting 
substance)  by  Buchner,  who  determined  also  that  the  alexin 
is  rapidly  decomposed  at  a  temperature  of  55°  C.  or  more. 

The  haemolytic  properties  of  the  blood-serum  of  an 
animal  are  increased  to  a  high  degree  if  the  animal  be  im- 
munised by  the  injection  of  erythrocytes  of  another  species. 
The  haemolytic  action  is  in  this  case  specific  against  ery- 
throcytes of  the  variety  employed  in  the  injections.  This 
observation  was  made  by  Bordet,2  who  found  also  that  the 
haemolytic  properties  vanish  after  heating  for  thirty  min- 

1  Landois:  "Die  Transfusion  des  Blutes,"  Leipzig,  1875,  cited  from  Hans 
Sachs:    "Die   Hamolysine"   in   Lubarsch-Ostertag's   Ergebnisse   d.   pathol. 
Anatomic,  Vol.  7,  1902.     This  memoir  contains  a  review  of  the  literature  on 
this  subject  up  to  that  time,  and  of  the  results  attained. 

2  Bordet:  Ann.  de.  I  hist.  Pasteur,  12  (1898). 

218 


THE  COMPOUND   H^MOLYSINS  2 19 

utes  to  55  °  C.,  but  may  be  restored  by  the  addition  of 
normal  serum. 

The  action  of  such  an  immune-serum  is  augmented  by 
the  addition  of  fresh  serum,  as  Ehrlich  and  Morgenroth l 
found,  and  the  haemolytic  power  of  the  heated  immune- 
serum  may  after  the  addition  of  normal  serum  exceed 
many  times  that  of  the  original  immune-serum  before 
being  heated.  These  observations  led  to  the  opinion,  as 
was  said  above  (p.  20),  that  the  immune-serum  contained 
two  substances,  the  one  the  so-called  immune-body  (or 
amboceptor),  stable  at  55°  C.,  and  another,  the  alexin  (com- 
plement), present  even  in  normal  serum,  labile  and  de- 
stroyed at  55°. 

Moreover,  the  immune-serum  contains,  as  Bordet  found, 
a  substance  which  agglutinates  erythrocytes  of  the  injected 
variety.  This  agglutinin  resists  heating  to  60°  C.,  but 
loses  its  agglutinating  properties  at  70°  C. 

As  is  seen  from  the  experiments  considered  on  p.  150, 
the  immune-body  is  absorbed  by  the  erythrocytes  in  large 
measure.  If  the  quantity  of  immune-body  present  is  not 
very  great,  it  will  be  practically  completely  absorbed  by 
the  erythrocytes.  Therefore,  if  erythrocytes  are  shaken 
for  an  hour  with  their  specific  immune-serum  that  has  been 
heated,  this  serum  is  afterward  innocuous  to  other  ery- 
throcytes, even  after  alexin  has  been  added.  But  the 
erythrocytes  which  have  absorbed  the  immune-body  may, 
after  separation  from  the  serum  by  centrifugation,  be 
dissolved  on  adding  an  alexin  to  them. 

In  an  analogous  manner  it  is  possible  to  show  that  the 
alexin  is  not  absorbed  to  a  noteworthy  degree  by  the  ery- 

1  Ehrlich  and  Morgenroth :  Berliner  klin.  Wochtnschrift,  1899,  No.  22, 


220  LECTURES  ON  IMMUNITY 

throcytes.  For  if  these  have  been  shaken  for  an  hour 
with  alexin  and  have  thereafter  been  separated  from  the 
fluid,  they  remain  intact  on  the  addition  of  immune-body. 

Ehrlich  and  Morgenroth  have  performed  experiments 
on  the  binding  of  immune-body  and  alexin  that  have 
caused  a  great  deal  of  discussion,  but  have  not  been  ex- 
plained in  a  satisfactory  manner.1  If  the  hsemolytic  mix- 
ture of  the  two  substances  is  shaken  with  the  specific 
erythrocytes  at  low  temperature  (0-3°  C.)  for  an  hour,  the 
immune-body  (from  goat-serum)  is  absorbed  by  the  ery- 
throcytes (of  sheep),  the  alexin  remaining  alone  in  the 
solution.  The  experiment  succeeds  even  at  40°  if  the 
time  of  contact  between  .solution  and  corpuscles  is  re- 
stricted to  ten  minutes.  If  the  corpuscles  are  then  sus- 
pended in  physiological  salt-solution  a  moderate  haemolysis 
is  observed,  which  is  augmented  if  alexin  (normal  goat- 
serum)  be  added. 

Evidently  we  here  observe  a  case  of  velocity  of  reaction, 
in  which  the  immune-body  plays  nearly  the  same  r61e  as 
cholesterin  in  Ransom's  experiments  with  saponin.  A 
difference  is  that  the  immune-body  is  very  rapidly  and 
strongly  absorbed  by  the  erythrocytes,  which  is  evidently 
not  the  case  with  cholesterin.  At  low  temperatures  the 
velocity  of  reaction  between  immune-body  and  alexin  is 
imperceptible.  Therefore  no  measurable  part  of  the  alexin 
(which  to  a  slight  degree  is  taken  up  by  the  blood-corpus- 
cles) becomes  bound  by  the  immune-body.  But  at  higher 
temperatures  a  sufficient  quantity  of  haemolysin  is  formed 

1  Ehrlich  and  Morgenroth:  BerL  klin.  Wochenschrift,  No.  I  (1899); 
Gruber:  Munch,  med.  Wochemchrift,  Nos.  48-49  (1901),  No.  2  (1904);  Mor- 
genroth: Wiener  klin.  Wochenschrift>  No.  43  (1903),  No.  5  (1904). 


THE  COMPOUND   H^EMOLYSINS  221 

in  the  blood-corpuscles  to  cause  a  trace  of  laking.  As 
soon  as  the  alexin  is  bound,  new  quantities  of  it  diffuse 
into  the  blood-corpuscles.  Therefore  the  haemolysis  in- 
creases if  corpuscles  loaded  with  immune-body  are  treated 
with  fresh  alexin.  On  the  other  hand  Ehrlich  and  Mor- 
genroth  found  that  the  fluid  in  which  the  erythrocytes  had 
been  suspended  for  one  or  two  hours  at  o°  C.  contained 
alexin.  In  this  manner  they  showed  that  even  the  haemo- 
lysins  in  normal  sera  (for  instance  goat-serum  acting 
upon  guinea-pigs'  erythrocytes)  are  formed  by  the  union 
of  an  immune-body  and  an  alexin.  They  also  stated  that 
a  given  immune-body  combined  with  different  alexins  (nor- 
mal sera  from  different  animals)  gives  haemolysins  of  very 
different  haemolytic  power,  which  eventually  may  be  due  to 
many  different  circumstances. 

Ehrlich  and  Morgenroth  supposed  that  the  compound  of 
immune-body  and  alexin,  i.e.  the  haemolysin,  which  is  pres- 
ent in  the  mixture  of  their  solutions,  is  the  active  part  and 
that  it  is  chemically  bound  to  the  erythrocytes,  which  are 
regarded  as  if  they  were  molecules.  To  explain  the  failure 
of  the  reaction  at  o°  C.  they  supposed  that  the  haemolysin 
is  nearly  completely  dissociated  at  low  temperatures,  o°  C., 
but  not  at  40°  C. ;  this  presupposes  that  the  union  of  im- 
mune-body and  alexin  is  accompanied  by  an  extremely 
great  absorption  of  heat,  which  is  in  the  highest  degree 
improbable.  The  membrane  of  the  erythrocytes  is  evi- 
dently to  a  very  slight  degree  permeable  to  the  haemolysin  ; 
and,  therefore,  it  is  only  the  haemolysin  formed  inside  their 
membranes  which  exercises  a  poisonous  action  on  the 
corpuscles,  just  as  in  the  case  of  saponin  and  cholesterin. 
These  experiments  do  not  teach  us  anything  concerning 


222  LECTURES  ON   IMMUNITY 

the  presence  of  haemolysin  in  the  mixture  of  immune-body 
and  alexin. 

Overton  has  drawn  attention  to  the  fact  that  the  alkaloids 
are  much  more  toxic  to  cells  of  animal  or  vegetable  origin 
than  are  their  salts.  This  depends  upon  the  circumstance 
that  the  cell  membranes  are  permeable  to  the  alkaloids 
themselves,  but  not  so  to  their  salts,  or,  more  strictly  speak- 
ing, to  their  ions.  The  salts  are  poisonous  at  all  only  be- 
cause they  are  to  some  extent  hydrolysed  in  their  watery 
solutions;  and  therefore  the  salts  of  the  weak  acids  are 
more  poisonous  than  those  of  the  strong  acids.  Under 
these  circumstances  an  excess  of  acid  diminishes  the  toxic- 
ity  of  these  salts,  even  to  the  point  of  complete  suppres- 
sion of  toxic  action.  On  the  other  hand,  the  presence  of 
substances  with  alkaline  reaction  sets  the  alkaloid  free,  and 
thus  increases  the  toxicity  of  the  solution  of  the  salt  of  an 
alkaloid.  (Cf .  Hoeber,  Physikalische  Chemie  der  Zelle  und 
Gewebe,  2d  ed.,  1906,  p.  165.) 

In  some  cases,  which  seem  to  be  rather  rare,  the  absorp- 
tion of  the  immune-body  by  the  erythrocytes  is  by  far  not 
so  evident  as  in  the  ordinary  case  represented  by  the 
figures  above  (p.  1 50).  Ehrlich  and  Sachs *  describe  some 
experiments  on  the  action  of  a  mixture  of  inactivated  ox- 
serum  and  normal  horse-serum  on  guinea-pigs'  erythro- 
cytes. These  are  at  37°  C.  laked  by  the  said  mixture 
within  one  hour.  But  if  the  erythrocytes  are  suspended 
for  one  hour  at  37°  C.  in  the  ox-serum,  and  then  after 
centrifugation  mixed  with  the  horse-serum,  no  such  re- 
sult is  observed. 

Ehrlich  explains  this  observation  as  due  to  the  circum- 

1  Ehrlich  and  Sachs:  Berl.  klint  Wochenschrifa  No,  31  (1902). 


THE  COMPOUND   H^MOLYSINS  223 

stance  that  the  corpuscle  has  no  affinity  for  the  immune- 
body  until  it  is  bound  to  the  alexin.  Evidently  this  is  only 
a  very  artificial  circumscription,  and  no  real  explanation. 
Bordet,  however,  later  on  proved  that  even  in  this  case 
the  immune-body  is  absorbed ;  to  his  investigation  on  this 
subject  we  shall  return  later  (cf.  p.  260). 

The  first  theoretical  view  of  these  phenomena  was  given 
by  Bordet,1  who  regarded  the  immune-body  as  a  kind  of 
catalytic  agent,  which  "  sensibilised "  the  erythrocytes  to 
the  attack  of  the  alexin.  The  objection  that  alexin  alone 
does  not  attack  the  erythrocytes  is  evidently  untenable. 
Bordet  advanced  his  experiment  on  the  effect  of  a  fraction- 
ated addition  of  haemolytic  serum  (cf.  p.  34)  to  a  given 
portion  of  erythrocytes  as  pleading  in  favour  of  his  idea. 
This  experiment  indicated  that  the  binding  to  the  cells 
does  not  take  place  in  constant  proportion,  as  Ehrlich 
tacitly  supposed.  But  Ehrlich  replied  that  the  cells  might 
bind  more  haemolysin  than  just  the  quantity  necessary  for 
laking.  Since  we  know  now  that  the  immune-body  is 
absorbed  by  the  erythrocytes,  this  controversy  has  only 
an  historical  interest.  In  a  certain  sense  we  must  allow 
Bordet  to  have  been  in  the  right,  the  entrance  of  the 
immune-body  into  the  erythrocytes  is  the  necessary  con- 
dition for  the  attack  of  the  alexin,  which,  as  we  shall  see 
later,  is  really  bound  to  equivalent  quantities  of  the  im- 
mune-body dissolved  in  the  erythrocytes.  Against  Bordet 
the  experiment  of  Ehrlich  and  Sachs  has  been  cited,  but 
this  is  easily  explained  by  the  view  that  the  immune-body 
is  absorbed. 

1  Bordet:  Annales  de  rinst.  Pasteur,  12.  688  (1898),  and  14.  257  (1900). 


224  LECTURES  ON  IMMUNITY 

An  experiment  of  Neisser  and  Wechsberg1  seems  to 
indicate  that  immune-body  and  alexin,  when  mixed,  really 
enter  into  a  compound,  at  least  partially.  They  used 
different  bacteriolysins,  which  like  the  haemolysins  are 
of  a  compound  nature,  so  that  the  presence  of  two  differ- 
ent substances,  an  immune-body  and  an  alexin,  is  neces- 
sary. They  used  a  constant  quantity  of  bacteria  and  of 
alexin,  to  which  they  added  different  quantities  of  immune- 
body.  At  first,  as  we  know,  the  action  increases  with  the 
concentration  of  the  immune-body,  but  finally  reaches  a 
maximum ;  and,  if  this  quantity  exceeds  a  certain  magni- 
tude the  effect  then  decreases,  so  that  the  bacteria  may 
even  not  be  destroyed.  This  phenomenon  has  been  called 
the  "diversion"  (Ablenkung)  of  the  alexin.  As  the  ex- 
periments with  bacteriolysins  are  not  very  well  adapted 
to  quantitative  experiments,  the  following  hsemolytic 
experiments  with  ox  erythrocytes,  immunised  rabbit- 
serum  as  immune-body,  and  guinea-pig-serum  as  alexin, 
may  serve  to  elucidate  the  relations.  In  the  following 
table  the  quantity  of  alexin  present  in  2.5  c.c.  of  solution 
is  called  b,  and  the  corresponding  quantity  of  immune- 
body  is  called  a.  As  unit  is  taken  the  thousandth  part  of 
the  quantity  contained  in  I  c.c.  of  the  two  original  prep- 
arations. The  quantity  of  erythrocytes  was  I  c.c.  of  a 
5  per  cent  suspension  of  ox  blood.  The  mixture,  which 
had  been  kept  for  thirty  minutes  at  24°  C,  was  allowed  to 
act  on  the  erythrocytes  for  two  hours  at  37°  C.  In  this 
manner  I  found  the  following  degrees  of  haemolysis  (com- 
plete haemolysis  =  100)  :  - 

1  Neisser  and  Wechsberg:  Munch,  med.  Wochenschrift  (1901). 


THE  COMPOUND   H^MOLYSINS  225 

ACTION  OF  DIFFERENT  QUANTITIES  OF  IMMUNE-BODY  ("DIVERSION") 


a  = 

b  =  10 

1=6 

3  =  4 

I 

31 

— 

— 

10 

45 

37 

30 

30 

100 

Si 

71 

5° 

100 

87 

65 

100 

100 

92 

64 

200 

100 

35 

15 

300 

64 

24 

7 

The  effect  is  very  evident.  The  maximum  in  the  three 
series  occurs  at  about  a  =  80,  50,  and  30  respectively. 
This  observation  seems  to  agree  very  well  neither  with 
the  views  of  Bordet  nor  with  those  of  Ehrlich.  If  the 
catalytic  agent  were  present  in  greater  quantity,  we 
might  expect  a  stronger  action,  but  the  reverse  is  the  case 
if  a  is  greater  than  100.  Now  according  to  Ehrlich's  view 
we  might  expect  that  the  active  substance,  the  hsemolysin 
which  is  here  preformed  in  the  mixture  and  thus  attacks 
the  corpuscles,  should  not  decrease  in  quantity  with  in- 
creasing concentration  of  immune-body,  and  therefore  the 
effect  should  be  just  as  according  to  Bordet's  theory.  Ehr- 
lich has  accepted  the  following  explanation  given  by 
Neisser  and  Wechsberg  for  their  experiment,  in  which  the 
bacteria  were  not  attacked  in  the  presence  of  an  excess  of 
immune-body.  "  If  a  is  large,  there  is  a  marked  excess 
over  the  quantity  of  alexin  (b),  so  that  all  the  alexin  is 
combined  as  lysin  (ab)  before  the  mixture  is  added.  The 
excess  of  a  is  then  bound  to  the  bacteria  (e)  and  gives  the 
compound  ea.  If  now  the  affinity  of  b  for  a  is  greater 
than  for  ea,  b  will  remain  as  lysin  (ab)  in  the  solution,  and 
Q 


226  LECTURES  ON  IMMUNITY 

not  pass  into  ea  to  give  the  compound  eab  which  gives 
bacteriolysis.  It  is  mere  chance  whether  the  affinity  of  b 
for  a  is  greater  than  for  ea,  as  in  this  case,  or  less,  in  which 
case  haemolysis  would  occur."  This  extremely  artificial 
explanation  seems  to  me  quite  erroneous.  For  if  we  have 
the  compounds  ea  and  ab  and  the  compound  eab  may  be 
formed,  its  formation  depends  wholly  upon  whether  e  has 
a  greater  affinity  for  ab  than  for  a.1  If  not,  then  eab  is 
not  formed,  even  if  a  is  not  present  in  excess.  Therefore, 
if  Ehrlich's  idea  were  right,  no  bacteriolysis  should  occur 
in  Neisser  and  Wechsberg's  experiments,  and  no  haemo- 
lysis in  the  experiments  cited  above. 

The  probable  cause  is  the  following.  If  a  is  large,  it  is 
not  totally  absorbed  by  the  cells,  but  a  fraction  of  it 
remains  in  the  surrounding  fluid,  and  this  part  increases 
rapidly  with  increasing  a  (cf.  p.  150).  a  forms  a  com- 
pound (ab)  with  b  as  well  outside  the  cells  as  within  them. 
This  compound  is  partially  dissociated,  so  that  its  quantity 
increases  and  the  quantity  of  free  alexin  b  decreases  with 
increase  of  a  in  the  liquid.  At  very  high  excess  of  a,  b 
may  become  practically  wholly  bound.  This  seems  to 
have  been  the  case  in  Neisser  and  Wechsberg's  experi- 
ment (the  errors  of  observation  are  too  great  to  give  a 
final  decision).  The  membranes  of  the  cells  are  (cf.  p.  22  r) 
practically  impermeable  to  the  lysin  (ab\  and  only  the 
lysin  formed  from  a  and  b  within  the  cells  is  active.  As 
there  is  now  very  little  (or  practically  no)  free  b  in  the 

1  It  is  assumed  that  the  amount  of  a  exceeds  the  quantity  which  is  neces- 
sary to  bind  (produce  lysis  with)  the  quantities  e  and  b.  This  necessary 
quantity  of  a  is  rather  unimportant,  about  2  in  my  experiments  cited  above, 
and  even  in  Neisser  and  Wechsberg's  experiments  this  condition  has  proba- 
bly been  fulfilled  long  before  a  gave  a  maximum. 


THE  COMPOUND  ILEMOLYSINS  22? 

solution,  b  cannot  diffuse  into  the  cells  during  the  given 
time  of  the  experiment  and  produce  a  lysis,  whereas  a  is 
present  there  in  many  times  the  necessary  quantity.  If 
a  decreases,  but  not  so  much  so  that  the  quantity  necessary 
for  the  lytic  action  is  not  absorbed  by  the  cells,  then  b 
increases  in  the  surrounding  fluid  and  a  greater  quantity 
of  it  diffuses  into  the  cells  within  a  given  time.  There- 
fore the  quantity  of  ab  present  in  the  cells  may  increase 
with  decreasing  quantity  of  a,  if  this  substance  be  present 
in  great  excess  in  the  surrounding  fluid.  The  presence  of 
a  maximum  is  therefore  quite  easy  to  understand.  The 
very  great  flatness  of  the  curve  of  this  maximum  indicates 
that  the  haemolysin  ab  is  stable  only  in  the  presence  of  a 
large  excess  of  a  and  b\  and  that  a  binding  of  strong 
affinities  with  sharp  discontinuities,  as  Ehrlich  supposes, 
is  excluded.  Our  view  leads  furthermore  to  the  conclu- 
sion that  the  effect  observed  by  Neisser  and  Wechsberg 
should  be  more  prominent  for  low  values  of  b  than  for 
larger  values.  The  quantity  of  diffusing  free  alexin  is  in 
the  first  approximation  proportional  to  b.  This  quantity 
is  therefore  proportional  also  to  the  quantity  of  haemolysin 
formed  in  the  given  time  of  action  (two  hours  at  37°  C. 
and  the  time  of  sedimentation  at  lower  temperature, 
about  3°  C.).  With  large  quantities  of  alexin  (b>2O  in 
the  present  case),  the  diffusion  transports  enough  of 
alexin  during  the  time  of  action  to  cause  total  haemolysis, 
even  at  the  highest  concentrations  of  a  employed. 
Further,  it  is  evident  that  as  the  quantity  of  free 
alexin  is  nearly  proportional  to  b  and  inversely  propor- 
tional to  a,  nearly  the  same  effect  will  be  reached  if  -  is  a 

a 


228  LECTURES  ON  IMMUNITY 

constant.  This  is  actually  found  to  be  the  case ;  for  in- 
stance, the  degree  of  haemolysis  64  corresponds  to  the  fol- 
lowing values  of  -:  =  0.033, =  0.04,  and-^-  =  0.04. 

a    300  150  100 

This  is  evidently  true  only  if  the  haemolytic  action  is  of 
such  a  magnitude  as  it  is  possible  to  reach  with  the  quan- 
tity of  b  present ;  and  this  circumstance  indicates  that  the 
said  rule  is  only  a  rather  rough  approximation.  The  rule 
stated  leads  to  the  consequence  that  the  maximum  appears 
at  a  lower  value  of  a  for  a  lower  value  of  b,  and  the  values 
of  a  at  the  maximum  are  nearly  proportional  to  the  value 
of  b  (80  :  10  =  8  ;  50  :  6  =  8.3  ;  30  :  4  =  7.5). 

It  had  been  observed  in  different  investigations  that 
the  quantity  of  alexin  necessary  to  produce  complete 
haemolysis  is  the  less  the  greater  the  quantity  of  immune- 
body  that  had  been  used  for  the  "  sensibilisation  "  of  the 
erythrocytes.1  This  matter  was  subjected  to  a  closer 
investigation  by  Morgenroth  and  Sachs.2  They  found 
that  in  one  case  (viz.  haemolysis  of  sheep  erythrocytes  by 
means  of  immune-bodies  from  goat  blood  and  alexin 
from  guinea-pig  serum)  the  quantity  (b)  of  alexin  was 
often  nearly  inversely  proportional  to  the  quantity  (a)  of 
immune-body  used.  In  another  case  (haemolysis  of  ery- 
throcytes from  ox  blood  with  immune-body  from  goat- 
serum  and  an  alexin  from  serum  of  guinea-pig  or  of  rabbit 
or  even  of  sheep)  the  quantity  of  alexin  necessary  for  com- 
plete haemolysis  was  independent  (or  nearly  so)  of  the 
quantity  of  immune-body  used.  In  other  cases  the  same 

Jv.  Dungern:  Munch,  med.  Wochenschrift,  No.  20  (1900);  Gruber: 
Wiener  klin.  Wochenschrift^Q.  15  (1902). 

2  Morgenroth  and  Sachs:  Berl.  klin.  Wochenschrift,  No.  35  (1902). 


THE  COMPOUND  H^MOLYSINS 

was  true  except  when  the  quantity  a  was  very  low.  To 
explain  this  very  different  behaviour  in  different  cases  the 
authors  have  made  use  of  rather  complicated  hypotheses, 
to  enter  in  detail  upon  which  would  consume  too  much 
space.  These  experiments  were  the  first  quantitative 
measurements,  on  a  large  scale,  bearing  upon  the  action 
of  compound  haemolysins,  and  they  therefore  merit  a 
certain  interest. 

Another  observation  of  quantitative  nature  was  made  by 
Morgenroth.1  He  determined  the  least  quantity  of  alexin 
that  had  to  be  added  to  produce  complete  haemolysis,  and 
the  greatest  quantity  of  alexin  which  could  be  added  before 
a  perceptible  haemolysis  occurred.  In  this  case  immune- 
body  was  present  in  excess.  In  other  cases  alexin  was 
present  in  excess,  and  the  quantities  of  immune-body 
necessary  for  complete  haemolysis  and  for  the  first  trace 
of  haemolysis  were  observed.  Morgenroth  found  that  the 
two  said  quantities  of  alexin  were,  as  the  average  of  13 
combinations,  in  the  proportion  100  to  13.6;  and  the  cor- 
responding quantities  of  immune-body  in  the  proportion 
100  to  14.1  (mean  of  10  combinations).  If,  as  is  rather 
probable,  the  quantity  of  haemolysin  found  is  nearly  pro- 
portional to  the  quantities  of  alexin  or  of  immune-body 
used,  and  the  rule  holds  that  the  degree  of  haemolysis  is 
proportional  to  the  square  of  acting  haemolysin,  this  would 
indicate  that  an  haemolysis  of  2  per  cent  is  just  perceptible, 
which  in  some  cases  may  be  rather  probable. 

Quite   recently   Wilfred   H.   Manwaring2  has   given   a 

1  Morgenroth :    Wiener  klin.  Wochenschrift,  No.  5  (1904). 
'2 Manwaring:  Journ.  Biol.  Chemistry,  1.  213  (1906).     No  definite  indi- 
cation is  given  of  the  nature  of  the  preparations  employed. 


230 


LECTURES  ON  IMMUNITY 


curve  representing  the  degree  of  haemolysis  by  means  of 
different  quantities  of  immune-body  in  the  presence  of  a 
great  excess  of  alexin.  It  may  here  even  be  assumed 
that  the  quantity  of  haemolysin  found  is  proportional  to  the 
quantity  of  immune-body.  The  following  figures  are  taken 
from  the  original  curve.  H  is  the  degree  of  haemolysis, 
A  the  quantity  of  immune-body. 

HAEMOLYSIS  BY   MEANS  OF  DIFFERENT  QUANTITIES   OF   IMMUNE-BODY 


A 

H 

Sa 

SH-.A 

I 

°-5 

0.71 

0.71 

2 

I 

i 

o-5 

3 

i-S 

1.23 

0.41 

4 

2 

1.41 

o-35 

5 

2-5 

1.58 

0.32 

6 

3 

'•73 

0.29 

7 

4 

2.0 

0.29 

8 

6 

2-45 

0.31 

9 

9 

3-o 

0-33 

10 

22 

4.69 

0.47 

ii 

35 

5-92 

0-54 

12 

47 

6.86 

o-57 

13 

58 

7.62 

o-59 

14 

68 

8.25 

o-59 

15 

79 

8.89 

o-59 

16 

84 

9.17 

0-57 

17 

86 

9.27 

0-55 

18 

90 

9-49 

0-53 

19 

93 

9.64 

0.51 

20 

97 

9.85 

0.50 

21 

99 

9-95 

0.47 

22 

IOO 

10.0 

0-45 

Between  the  degrees  of  haemolysis  35  and  90,  i.e.  within 
two-thirds  of  the  interval  examined,  a  remarkable  propor- 
tionality between  the  square  root  of  the  degree  of  haemoly- 
sis and  the  quantity  of  immune-body  is  observed.  With 


THE  COMPOUND  H^MOLYSINS  231 

lesser  quantities  of  immune-body,  the  haemolysis  is  not  so 
great  as  this  rule  predicts,  and  this  corresponds  to  the 
behaviour  of  other  lysins  (cf.  pp.  103  and  169),  except  that 
the  deviation  from  the  rule  in  this  case  is  evident 
throughout  the  wide  interval  from  o  to  30  per  cent,  where 
as  for  other  lysins  the  deviation  is  observed  only  under 
10  or  15  per  cent. 

In  the  memoirs  cited  Morgenroth  and  Morgenroth  and 
Sachs  employed,1  among  other  hypotheses  to  explain  their 
observations,  this  also,  that  immune-body  and  alexin  some- 
times enter  into  a  compound  haemolysin  or  haemolysin 
united  with  an  erythrocyte,  which  is  stable  only  in  the  pres- 
ence of  considerable  quantities  of  the  components.  These 
different  substances  participate,  according  to  the  Frankfort 
school,  in  a  chemical  equilibrium.  On  the  other  hand,  the 
adherents  of  Bordet,  among  whom  Metchnikoff,  Gruber, 
and  Biltz  may  be  cited,  regard  the  haemolytic  action  as  a 
phenomenon  of  absorption.  It  seemed  possible  to  decide 
by  means  of  quantitative  experiments  which  of  these  two 
ideas  corresponds  to  the  facts,  and  Ehrlich  invited  me  to 
undertake  an  investigation  of  this  point  in  the  laboratory 
of  the  serum  institute  in  Frankf  ort-on-the-Main.  These  in- 
vestigations led  to  the  very  certain  conclusion  that  a  chemi- 
cal equilibrium  governs  the  reaction  of  immune-body  and 
alexin,  but  the  important  reaction  takes  place  within  the 
erythrocytes.  It  is  very  probable  also  that  such  an  equi- 
librium exists,  even  in  the  mixture  of  immune-body  and 
alexin,  as  is  indicated  by  the  diminution  of  the  haemolytic 
effect  with  increasing  immune-body,  as  noted  in  some  cases 

1  Morgenroth:  Wiener  klin.  Wochenschrift,  No.  43,  p.  5  (1903);  Mor- 
genroth and  Sachs:  Berl klin.  Wochcnschrift,  No.  35,  p.  8  (1902). 


232  LECTURES  ON  IMMUNITY 

(cf.  p.  225).  And  it  is  even  probable  that  the  haemolysin 
enters  into  combination  with  the  molecules  of  the  proto- 
plasm inside  the  erythrocytes,  just  as  tetanolysin  or  alka- 
lies do  (cf.  pp.  103  and  no);  but  concerning  this  reaction 
we  learned  very  little  or  nothing  from  my  experiments. 

My  measurements  were  founded  upon  determinations 
of  the  degree  of  haemolysis  exerted  by  a  given  mixture  of 
immune-body  and  alexin  acting  upon  a  given  quantity 
of  erythrocytes.  To  this  end  i  c.c.  of  a  5  per  cent  sus- 
pension of  erythrocytes  (from  sheep  or  ox)  in  physio- 
logical solution  of  NaCl  was  mixed  with  1.5  c.c.  of  a  fluid 
containing  the  desired  quantities  of  immune-body  and 
alexin  and  additional  physiological  salt-solution  until  the 
total  volume  was  always  2.5  c.c.  All  the  preparations  were 
kindly  supplied  by  the  Institute. 

After  the  blood  suspension  and  the  haemolytic  mixture 
had  been  each  mixed  thoroughly  by  shaking  (for  reasons 
referred  to  above,  cf.  p.  15),  the  cell  suspension  was 
poured  into  the  mixture  in  a  rapid  manner,  the  test-tubes 
containing  the  mixture  were  placed  in  an  incubator  at  37°  C. 
for  2  hours,  after  which  time  the  test-tubes  were  taken  out 
and  set  into  a  refrigerator  at  about  2°  C.,  where  they 
remained  until  the  next  morning  (about  17  hours),  when 
they  were  examined  and  the  degree  of  haemolysis  deter- 
mined by  comparison  with  test-tubes  containing  different 
quantities  of  the  same  variety  of  erythrocytes,  laked  in 
distilled  water. 

The  immune-body  and  the  alexin  were  left  together  for 
about  half  an  hour  at  room  temperature  (20-24°  C.)  before 
the  addition  of  the  cell  suspension,  but  the  time  of  reaction 
between  these  two  substances  seemed  not  to  have  a  per- 


THE  COMPOUND  H^EMOLYSINS  233 

ceptible  influence,  as  special  experiments  indicated.  As 
has  been  said,  probably  the  chemical  reaction  takes  place, 
at  least  chiefly,  in  the  interior  of  the  red  blood-corpuscles, 
and  under  such  circumstances  it  is  easy  to  understand 
that  the  time  of  reaction  between  immune-body  and  alexin 
prior  to  the  addition  of  the  blood  is  of  little  or  no  conse- 
quence. Since  we  know  the  haemolysed  quantity,  we  wish 
to  calculate  from  it  the  quantity  of  haemolysin.  For  this 
purpose  we  may  employ  the  rule  that  the  hasmolysed  quan- 
tity is  nearly  proportional  to  the  square  of  the  quantity  of 
acting  haemolysin.  If  this  rule  for  low  concentrations 
of  haemolysin  does  not  lead  to  quite  exact  results,  this 
result  does  little  harm,  for  the  chief  thing  is  to  find 
instances  in  which  the  quantity  of  haemolysin  is  the 
same,  and  this  occurs,  evidently,  as  soon  as  the  degree 
of  haemolysis  is  the  same.  Approximately  the  quantity 
of  haemolysin  is  proportional  to  the  square  root  of  the 
known  quantity  of  haemolysis.  In  reality  we  make  use 
of  this  rule  only  in  order  to  set  forth  the  observations  in 
a  simple  manner. 

As  illustration  I  reproduce  here  a  series  of  experiments 
with  red  blood-corpuscles  from  the  ox.  The  immune-body 
was  prepared  by  injection  of  such  erythrocytes  into  the 
veins  of  a  goat.  The  alexin  was  normal  serum  of  guinea- 
pigs.  The  arbitrary  units  employed  are  o.ooi  of  a  c.c. 
of  the  preparations  containing  immune-body  or  serum  of 
guinea-pigs.  The  unit  of  haemolysin  is  a  hundredth  part 
of  the  quantity  necessary  for  total  haemolysis  of  the  fixed 
quantity  of  blood-corpuscles.  The  first  of  the  following 
series  gives  the  observed  haemolysed  quantities,  the  second 
the  quantities  of  haemolysin  (square  root  of  the  foregoing 


234 


LECTURES  ON  IMMUNITY 


multiplied  by  100).  In  parentheses  are  tabulated  the  calcu- 
lated values  of  the  same  quantities  according  to  the  for- 
mula :  — 

(5  a  —  x)  (20  b  —  x)  —  gox. 

Where  a  is  the  quantity  of  immune-body  added,  and 
b  the  corresponding  quantity  of  alexin,  x  is  the  quantity 
of  haemolysin  formed. 

EQUILIBRIUM  BETWEEN  IMMUNE-BODY  FROM  GOAT,  ALEXIN  FROM 
GUINEA-PIG,  AND  H^MOLYSIN  FOR  Ox  ERYTHROCYTES 

A.       HAEMOLYSIS 


a  — 

10 

30 

100 

300 

900 

6=60 

16  (21) 

— 

— 

— 

— 

40 

14  (20) 

— 

— 

— 

— 

25 

I4(l8) 

— 

- 

— 

— 

15 

15   (14) 

—  * 

— 

— 

— 

10 

14  (10) 

50  (7°) 

96  (100) 

100  (100) 

— 

6 

5(6) 

35  (36) 

72  (96) 

96  (100) 

— 

4 

4(4) 

20  (19) 

56  (43) 

67  (53) 

— 

2-5 

— 

6(8) 

26  (18) 

22  (22) 

— 

i-5 

— 

2(3) 

6(6) 

5(8) 

6(9) 

i 

— 

— 

2(3) 

2(3) 

3(4) 

0.6 

— 

— 

1(0 

2(0 

2(1) 

B.    QUANTITY  OF  H^MOLYSIN 


a  — 

10 

3° 

TOO 

3oo 

900 

b=6o 

40  (46) 

— 



— 

— 

40 

37  (45) 

— 



— 

— 

25 

38  (42) 

— 



— 

— 

15 

39  (37) 

— 



— 

— 

10 

38  (33) 

71  (84) 

98  (100) 

100  (lOO) 

— 

6 

22  (25) 

59(60) 

85  (98) 

98  (100) 

— 

4 

20  (20) 

45  (44) 

75  (66) 

82  (73) 

— 

2-5 

— 

24  (29) 

51  (43) 

47  (47) 

— 

i-5 

— 

15  08) 

25  (25) 

22  (28) 

24  (29) 

i 

— 

— 

15  (17) 

15  09) 

18  (20) 

1.6 

— 

— 

II  (10) 

I3(n) 

13  (12) 

THE  COMPOUND  H^MOLYSINS  235 

As  will  be  seen  from  these  figures,  the  agreement  be- 
tween experiment  and  calculation  is  very  satisfactory  and 
the  differences  lie  within  the  possible  errors  of  observation. 
For  low  values  of  x,  the  observed  values  are  generally  less 
than  the  calculated  ones,  which  may  be  due  to  the  devia- 
tion from  the  rule  of  square  roots.  The  time  of  reaction 
was  long  enough  to  yield  nearly  the  limit  value  of  the 
reaction,  so  that  it  was  not  necessary  to  measure  the  time 
with  great  exactitude. 

If,  now,  the  immune-body  acted  like  a  catalytic  agent, 
we  might  expect  that  the  haemolysis,  at  a  constant  concen- 
tration of  immune-body,  would  increase  with  the  quantity 
of  alexin,  as  it  indeed  does  if  the  quantity  of  immune-body 
is  not  very  low.  But  if  the  quantity  of  alexin  is  sufficient 
for  total  haemolysis(£  >  5),  then  the  reaction  should  attain 
total  haemolysis  more  slowly  with  low  quantities  of  immune- 
body  and  more  rapidly  with  higher  quantities. 

For  small  quantities  of  immune-body  the  limit  of  reaction 
would  therefore  not  be  reached  before  total  haemolysis  was 
attained,  as  soon  as  b  >  5.  This  does  not  agree  at  all  with 
experience.  With  small  quantities  of  immune-body  the 
haemolysis  shows  itself  to  be  nearly  independent  of  the 
added  quantity  of  alexin  as  soon  as  this  exceeds  a  certain 
quantity  (b  >  10).  This  can  be  explained  only  by  assuming 
a  chemical  reaction  in  which  the  immune-body  contributes 
material  to  the  formation  of  haemolysin.  With  low  quan- 
tities of  immune-body  there  cannot  be  formed  a  greater 
quantity  of  haemolysin  than  is  equivalent  to  the  available 
quantity  of  immune-body;  the  added  quantity  of  alexin  may 
be  of  any  magnitude.  This  corresponds  very  well  with 
the  observations  and  the  same  reasoning  is  evidently  valid 


236  LECTURES   ON   IMMUNITY 

for  the  alexin.  If  it  be  added  in  small  quantity,  there 
cannot  be  formed  more  than  the  equivalent  quantity  of 
haemolysin.  This  property  is  also  very  evident  from  the 
measurements. 

Much  better  than  all  general  considerations  do  the 
agreements  between  the  values  calculated  from  the  for- 
mula and  the  observed  values  indicate  the  correctness  of 
the  view  adopted.  This  formula  indicates  also  that  one 
unit  of  the  haemolysin  (that  is,  the  hundredth  part  of  the 
quantity  necessary  to  haemolyse  completely  i  c.c.  of  a 
5  per  cent  suspension  of  bovine  red  blood-corpuscles)  is 
equivalent  to  the  fifth  part  of  a  unit  of  immune-body 
and  to  the  twentieth  part  of  a  unit  of  alexin.  The  cir- 
cumstance that  the  quantity  of  haemolysin  is  to  be  sub- 
tracted from  the  quantity  of  added  immune-body  and 
alexin,  recalculated  to  equivalent  quantities,  shows  that 
both  substances  are  consumed  in  the  formation  of  the 
haemolysin.  The  form  of  the  equation  indicates  also 
that  one  molecule  of  immune-body  and  one  molecule  of 
alexin  form  one  molecule  of  haemolysin. 

Another  illustration  is  red  corpuscles  from  sheep  blood 
attacked  by  a  haemolysin  formed  of  an  immune-body  from 
a  goat  injected  with  sheep  blood,  and  alexin  in  serum 
from  guinea-pigs.  The  quantity  of  haemolysin,  x,  was  cal- 
culated with  the  formula  :  — 

(40  a  —  x)  (25  b  —  x)=  1900 x. 

I  give  only  the  series  for  the  observed  haemolysis. 

The  agreement  between  the  observed  and  calculated 
values  is,  as  in  the  preceding  illustration,  as  good  as  could 
be  desired,  that  is,  within  the  possible  experimental  errors. 


THE  COMPOUND   H^iMOLYSINS 


237 


HAEMOLYSIS  OF  ERYTHROCYTES  FROM  SHEEP  BY  IMMUNE-BODY  FROM  GOAT 
AND  ALEXIN  FROM  GUINEA-PIG 


a  = 

i 

3 

10 

3° 

100 

300 

1000 

b  =  6o 

5(4) 

— 

— 

— 

— 

— 



40 

5(2) 

17  (16) 

— 

— 

— 

— 

— 

25 

2(2) 

15(9) 

60  (75) 

— 

— 

— 

— 

15 

— 

5(4) 

35  (33) 

95  («») 

— 

— 

— 

10 

1(0-3) 

3(2) 

20  (16) 

80  (85) 

95  (I0°) 

— 

— 

6 

— 

2(1) 

7(6) 

35  (30 

75  (10°) 

100  (100) 

100  (lOO) 

4 

— 

— 

3(3) 

1505) 

35  (44) 

80  (75) 

70  (90) 

2-5 

— 

— 

— 

7(6) 

I5(i7) 

30  (30) 

50  (36) 

i-5 



— 

— 

— 

4(6) 

4(10) 

17  (13) 

i 

— 

— 

— 

— 

— 

2(4) 

3(6) 

It  may  perhaps  seem  strange  that  greater  quantities  of 
alexin  have  not  been  used,  but  the  normal  serum  of  guinea- 
pigs  in  itself  contains  a  little  haemolysin,  so  that  it  is  nec- 
essary to  introduce  a  correction  for  this  action ;  a  simple 
subtraction  was  used.  For  greater  concentrations  of  alexin 
the  corrections  would  be  rather  great,  and  as  they  are 
always  accompanied  by  some  uncertainty,  it  seemed  best 
not  to  use  such  concentrations. 

Even  in  this  case  the  formula  indicates  that  from  one 
molecule  of  immune-body  and  one  molecule  of  alexin  one 
molecule  of  haemolysin  is  formed.  This  is  not  always  the 
case,  as  will  be  seen  from  the  following  examples.  The  in- 
dicator used  was  bovine  red  blood-corpuscles ;  the  immune- 
body  was  prepared  from  the  blood  of  a  rabbit  injected  with 
bovine  corpuscles ;  the  alexin  was  normal  serum  from  the 
guinea-pig.  The  arrangement  of  the  experimental  series 
was  quite  the  same  as  in  the  instances  treated  above.  The 
values  concern  the  haemolysis. 

Here  we  meet  with  the  exponent  f ,  which  seems  to  be 
common  in  this  domain.  The  equation  indicates  that  two 


238 


LECTURES  ON  IMMUNITY 


molecules  of  immune-body  with  three  molecules  of  alexin 
yield  six  molecules  of  hsemolysin. 

H^MOLYSIS  OF  BOVINE  ERYTHROCYTES  BY  IMMUNE-BODY  FROM  RABBIT 
AND  ALEXIN  FROM  GUINEA-PIG 


a  = 

0.4 

i 

IO 

5° 

IOO 

300 

=  60 

12  (II) 

32  (35) 

— 

— 

— 

— 

40 

12  (10) 

27  (26) 

IOO  (lOO) 

— 

— 

— 

25 

5  (7) 

18  (17) 

70  (83) 

— 

— 

— 

15 

3  (5) 

6  (ii) 

40  (44) 

— 

90  (loo) 

— 

10 

— 

5  (7) 

27  (27) 

— 

70  (59) 



6 

— 

2  (4) 

12  (I3) 

40  (22) 

22  (26) 

— 

4 

— 

i  (3) 

4  (7) 

10  (10) 

3  (12) 

10  (I4) 

2-5 

— 

— 

2  (3) 

3  (5) 

2  (5) 

5  (6) 

The  equation  used  for  the  calculation  has  the  form  :  — 
(1000  — *)*(iO  b  —  x)=  i.  a*2. 

H/EMOLYSIS   OF   ERYTHROCYTES   FROM   Ox   BY   MEANS   OF   COBRA-LECITHID 


LECITHIN  = 

2 

3 

10 

50 

IOO 

Cobra  =250 

88  (94) 

— 

— 

— 

— 

15° 

80  (57) 

IOO  (lOO) 

— 

— 

— 

IOO 

32  (37) 

72  (79) 

— 

— 

— 

75 

32  (28) 

64  (59) 

— 

— 

— 

50 

20  (20) 

36  (39) 

IOO  (lOO) 

— 

— 

35 

10  (13) 

32  (28) 

88  (87) 

— 

— 

25 

8(9) 

32  (20) 

66  (62) 

IOO  (lOO) 

— 

15 

— 

8  (12) 

36  (38) 

72  (84) 

— 

10 

— 

4  (8) 

— 

60  (56) 

IOO  (IOO) 

7-5 

— 

— 

— 

40  (42) 

68  (96) 

5 

— 

— 

— 

36  (28) 

64  (64) 

3-5 

— 

— 

— 

4  (20) 

40  (45) 

2-5 

— 

— 

— 

— 

40  (32) 

i-5 

— 

— 

— 

— 

32  (16) 

i 

— 

— 

— 

— 

24  (13) 

In  all  these  cases  the  immune-body  and  the  alexin  are 


THE  COMPOUND  H.EMOLYSINS  239 

consumed  to  a  sensible  degree  in  the  formation  of  the 
haemolysin.  Therefore  in  the  formulae  x  is  always  sub- 
tracted from  the  equivalent  quantity  of  immune-body  and 
alexin.  In  another  simikr  case,  namely,  the  formation  of 
the  haemolytic  substance  cobra-lecithid  from  cobra-poison 
and  lecithin,  the  quantity  of  haemolysin  seems  always  to 
be  so  small  that  it  makes  no  difference  if  it  be  subtracted 
from  the  quantities  of  cobra-poison  and  lecithin  or  not. 
The  experiments  were  carried  out  with  a  o.  i  per  cent  solu- 
tion of  cobra-poison  (i  c.c.  =  10,000  units)  and  a  i  per  cent 
solution  of  lecithin  (i  c.c.  =  1000  units).  The  arrange- 
ment of  the  table  is  the  same  as  in  the  foregoing. 

The  calculated  values  were  obtained  with  the  aid  of  the 
formula :  — 

C (L-  i. 5)1  =  6.67*2  =  6.67/2, 

where  C  represents  the  quantity  of  cobra-poison  added,  L 
the  corresponding  quantity  of  lecithin,  x  the  quantity  of 
haemolysin  formed,  and  h  the  observed  quantity  of  haemo- 
lysis tabulated  above.  As  will  be  seen  from  the  equation, 
no  haemolysis  occurs  until  1.5  units  of  lecithin  have  been 
added.  This  quantity  was  determined  by  special  experi- 
ments. The  experiments  with  cobra-lecithid  indicate  that 
this  poison  behaves  a  little  differently  than  the  other 
haemolysins.  With  these  a  limit  of  the  reaction  was  prac- 
tically reached  on  standing  for  two  hours  in  an  incubator 
at  37°  C.,  and  afterwards  for  seventeen  hours  in  a  refrig- 
erator. But  in  the  case  of  cobralysin,  haemolysis  continued 
in  the  sedimented  blood-corpuscles  after  the  observations 
cited  above  were  ended,  so  that  the  result  was  wholly  dif- 
ferent after  an  additional  twenty-four  hours,  during  the 


240  LECTURES  ON  IMMUNITY 

chief  part  of  which  time  the  temperature  was  2°  C.  The 
haemoglobin  that  had  passed  out  in  the  last  twenty-four 
hours  had  not  had  time  to  diffuse  throughout  the  liquid, 
but  remained  in  the  lowest  strongly  coloured  stratum. 
These  observations  suggest  strongly  that  the  haemolytic 
substance  was  absorbed  by  the  erythrocytes.  The  quantity, 
1.5,  of  lecithin  must  in  some  manner  be  bound  by  a  foreign 
substance  in  the  blood  suspension,  so  that  it  is  not  available 
for  the  cobra-poison. 

In  this  case  we  cannot  see  from  the  formula  that  cobra- 
poison  and  lecithin  are  consumed  for  the  formation  of  the 
cobra-lecithid.  This  must  therefore  be  dissociated  in  solu- 
tion to  an  extremely  high  degree,  and  the  least  quantities 
of  it  must  be  sufficient  to  produce  haemolytic  actions.  But 
precisely  for  this  case  Kyes  has  made  it  probable  that  a 
compound  —  cobra-lecithid  —  is  formed,  that  even  in  very 
small  quantities  produces  haemolysis.1 

The  power  f  for  the  quantity  of  lecithin  in  the  last 
formula  is  the  same  which  is  sometimes  found  for  the 
immune-body,  but  never  for  the  alexin.  This  seems  to  in- 
dicate that  the  lecithin  plays  the  same  r61e  as  the  immune- 
body  in  the  formation  of  the  haemolysin,  and  that  the 
cobra-poison  corresponds  to  the  alexin.  This  opinion 
seems  corroborated  by  the  fact  that  the  alexin  is  regarded 
as  the  properly  poisonous  substance  of  the  two,  and  it 
seems  more  natural  to  suppose  that  the  cobra-poison  is  the 
carrier  of  the  poisonous  properties,  than  that  the  innocuous 
lecithin  acts  haemolytically. 

Quite  recently  there  has  been  a  vivid  discussion,  if 
lecithin  exerts  an  influence  on  the  haemolytic  action  of  a 

1  Preston  Kyes:  Berl.  klin.  Wochenschrift,  Nos.  42  and  43  (1903). 


THE  COMPOUND   H^MOLYSINS  241 

very  simple  substance,  namely,  mercuric  chloride.1  As 
this  process  is  rather  perspicuous  and  indicates  the  mode 
of  action  of  lecithin,  we  will  take  it  under  consideration 
for  some  moments. 

In  weak  doses  mercuric  chloride  acts  haemolytically ;  in 
greater  concentration  it  agglutinates  the  erythrocytes  and 
the  haemolysis  is  weak  or  insensible.  At  a  certain  con- 
centration, therefore,  the  degree  of  haemolysis  passes 
through  a  maximum.  The  disappearance  of  the  haemo- 
lytic  action  at  higher  concentrations  is  regarded  as  due  to 
the  hardening  of  the  protoplasma  and  especially  of  the 
membranes  of  the  erythrocytes,  whereby  the  passage  of 
haemoglobin  through  it  is  hindered.  As  Sachs  has 
shown,2  it  is  possible  to  provoke  the  haemolysis  of  such 
hardened  erythrocytes  by  treating  them  with  solutions  of 
potassium  iodide  or  hyposulphite  of  sodium  or  of  albumen, 
which  all  take  away  a  deal  of  the  mercuric  chloride  from 
the  erythrocytes,  which  have  been  in  contact  with  a  solution 
of  this  substance. 

The  observed  maximum,  therefore,  in  this  case  depends 
upon  a  double  action  of  the  mercuric  chloride,  one  de- 
structive, whereby  the  erythrocytes  give  away  their  haemo- 
globin *-to  the  surrounding  fluid,  and  one  hardening, 
whereby  the  permeability  of  the  membranes  of  these 
cells  is  checked.  It  is  well  possible  that  other  similar 
cases,  in  which  maxima  are  observed,  as  for  instance  with 
the  botulismus-poison  or  with  mixtures  of  saponin  and 


1  Detre  and  Sellei:    Berl.  klin.  Woe  kens  chrift,  No.  30  (1904);    Wiener 
klin.    Wochens chrift,    Nos.    45   and  46    (1904);    No.   30   (1905).     Sachs: 

Wiener  klin.   Wochenschrift,  No.  35  (1905). 

2  Sachs:    Miinchner  medicinische  Wochenschrift,  No.  5  (1902). 


242  LECTURES  ON   IMMUNITY 

cholesterin,  may  be  due  to  a  secondary  action,  whereby 
the  velocity  of  the  process  is  retarded,  concurring  with 
the  chief  action  of  the  poison. 

Detre  and  Sellei  had  observed  that  the  haemolytic  action 
of  mercuric  chloride  is  diminished  by  the  presence  of 
lecithin.  Against  this  Sachs  stated  that  lecithin  ac- 
celerates the  action  of  mercuric  chloride.  Sachs  rightly 
holds  the  opinion  that  no  poisonous  combination  of  mer- 
curic chloride  and  of  lecithin  exists,  but  that  we  here 
observe  an  action  of  the  lecithin  on  the  erythrocytes, 
whereby  these  are  rendered  more  accessible  to  the  mer- 
curic chloride.  Here  we  find  that  Sachs  takes  up  the 
opinion  of  Bordet  regarding  the  sensibilisating  action  of 
certain  substances  on  erythrocytes.  Evidently  the  lecithin 
enters  into  the  cell-membranes  and  increases  their  per- 
meability to  the  haemoglobin  or  to  the  mercuric  chloride. 

According  to  this  observation  it  seems  obvious  to  sup- 
pose that  the  action  of  lecithin  on  erythrocytes  treated 
with  cobra-poison  is  due  to  a  similar  circumstance.  The 
slowness  of  the  hsemolytic  action  in  this  case  speaks  in 
favour  of  this  opinion.  If  the  chief  part  of  the  lecithin 
remains  in  the  fluid,  the  absorbed  part  in  the  membranes 
of  the  erythrocytes  is  proportional  to  the  f  power  of  the 
quantity  of  lecithin,  diminished  by  the  chemically  bound 
part  of  it.  The  results  given  above  regarding  the  action 
of  cobra-poison  in  presence  of  lecithin  will  then  be  under- 
stood if  we  make  the  very  plausible  hypothesis  that  the 
haemolytic  action  is  proportional  to  the  concentration  of 
the  cobra-poison,  and  further  that  the  permeability  of  the 
cell-membranes  is  proportional  to  the  absorbed  quantity 
of  lecithin. 


THE  COMPOUND  HJEMOLYSINS  243 

As  we  have  seen  before,  the  immune-bodies  in  the  rabbit 
treated  with  ox  erythrocytes,  and  in  the  goat  treated  with 
sheep  erythrocytes  are  almost  completely  absorbed  by 
the  red  blood-corpuscles  (cf.  p.  150)  in  weak  solutions. 
The  same  is  probably  the  case  for  the  immune-body  from 
a  goat  treated  with  ox  erythrocytes.  The  formation  of 
haemolysin  is,  without  doubt,  effected  only  in  the  red 
blood-corpuscles  themselves,  for  these  absorb  the  immune- 
body  before  a  reaction  takes  place  (cf.  p.  220).  On  the 
other  hand,  they  dissolve  very  little  of  the  alexin,  but  this 
is  combined  with  the  immune-body,  so  that  new  alexin 
enters  and  forms  the  poisonous  haemolysin.  The  circum- 
stance that  the  alexin  always  enters  to  the  power  i  would 
then  indicate  that  the  alexin  has  the  same  molecular  weight 
in  the  blood-corpuscle  and  in  the  surrounding  fluid,  so 
that  a  constant  fraction,  probably  very  little,  is  always  con- 
tained within  the  blood  corpuscles.  In  the  equation  of 
reaction  this  fraction  should  probably  be  introduced,  but 
if  instead  of  that  we,  as  in  the  formulae  above,  write  the 
whole  quantity  of  alexin,  that  has  no  other  effect  than  that 
the  constant  of  equilibrium  changes  in  a  certain  pro- 
portion. The  haemolysin  formed  probably  remains  for 
the  greatest  part  absorbed  in  the  red  blood-corpuscles. 

As  for  lecithin,  it  probably  enters  very  easily  into  the 
red  blood-corpuscles,  and  therefore  plays  the  r61e  of  an 
immune-body. 

The  action  of  the  compound  haemolysins  is  therefore,  like 
that  of  the  simple  haemolysins,  based  upon  their  presence 
in  the  red  blood-corpuscles,  which  are  thereby  so  changed 
that  the  membrane  becomes  permeable  to  haemoglobin. 

As  we  have  seen  before,  the  immune-body   at  higher 


244  LECTURES  ON  IMMUNITY 

concentrations  is  not  wholly  absorbed  by  the  erythrocytes, 
and  therefore  gives  a  compound  with  the  alexin,  even  out- 
side the  erythrocytes.  Thereby  we  explain  the  seeming 
anomaly  that  a  less  degree  of  haemolysis  may  be  pro- 
duced by  a  greater  quantity  of  immune-body  (cf.  p.  224). 
It  is  evident  that  equations  like  those  given  above  are  not 
able  to  reproduce  such  a  phenomenon.  The  same  effect 
may  even  exert  a  diminishing  influence,  though  to  a 
lesser  degree,  on  the  action  of  the  immune-body.  It  would 
therefore  be  conceivable  that  this  effect  is  responsible  for 
the  exponent  f  for  the  quantity  of  the  immune-body ;  and 
that  in  reality,  if  this  disturbing  effect  did  not  occur,  the 
first  power  of  the  said  quantity  would  result  from  the 
experiments.  This  opinion  seems  confirmed  by  the  fact 
that  the  exponent  f  occurs  precisely  for  the  combination  of 
immune-body  from  the  rabbit  treated  with  ox  erythrocytes 
and  alexin  from  guinea-pigs,  which  in  another  series  of 
experiments  —  with  different  preparations  —  gave  a  very 
pronounced  diversion  of  the  alexin.  But  this  explanation 
is  not  applicable  to  the  action  of  lecithin  in  the  experi- 
ments with  cobra-lecithid. 

My  experiments  show  that  even  in  this  case  a  remark- 
able regularity  governs  the  binding  of  immune-body  and 
alexin.  Therefore  it  has  not  been  necessary  for  me  to 
make  use  of  a  large  number  of  different  methods  of  ex- 
planation, as  Morgenroth  and  Sachs  did.  To  explain  the 
results  of  their  measurements  they  suppose  that  the  im- 
mune-body is  bound  to  the  erythrocytes  in  different 
manners,  that  the  affinity  of  immune-body  for  alexin  is 
altered  to  different  degrees  by  the  influence  of  the  erythro- 
cytes, and  that  the  immunised  sera  contain  a  great  number 


THE  COMPOUND   H^MOLYSINS  245 

of  different  immune-bodies.  "  We  observe  that  the  different 
phenomena  which  we  have  found  correspond  to  relative 
quantities  of  immune-bodies  and  alexins  (at  complete 
haemolysis)  may  have  very  different  causes,  but  that  they, 
if  we  regard  all  these  factors  related  above,  may  be  ex- 
plained in  an  unconstrained  manner."  1  On  the  other  hand, 
I  have  found  that  the  observed  phenomena  may  be 
explained  by  assuming  that  the  law  of  mass  action  governs 
the  equilibrium  of  reaction  between  immune-body  and 
alexin,  and  that  no  special  hypotheses  are  necessary  for 
the  special  cases.  It  may  even  be  regarded  as  very  prob- 
able that  a  closer  investigation  of  the  combinations  ex- 
amined by  Morgenroth  and  Sachs  would  have  led  them  to 
a  more  simple  explanation  than  that  which  they  have  pro- 
posed. 

We  have  stated  above  that  after  repeated  injections  of  a 
poison,  e.g.  ricin,  into  the  veins  of  an  animal,  e.g.  a  rabbit, 
the  serum  of  this  animal  contains  an  antitoxin,  in  this  case 
antiricin.  If  we  inject  this  antibody  into  the  veins  of 
another  animal,  e.g.  a  guinea-pig,  this  animal  is  said  to  be 
passively  immunised  against  ricin,  i.e.  its  blood-serum 
contains  the  injected  antiricin,  which  slowly  disappears 
(cf.  p.  4)  from  the  blood.  On  the  other  hand,  the  animal 
produces  an  antibody  against  the  antiricin,  as  may  be 
shown  by  experiments  with  mixtures  of  ricin,  antiricin, 
and  the  anti-antiricin.  Such  experiments  were  executed 
by  Bashford,2  who  even  says  that  some  of  his  experiments 
indicate  analogous  properties  of  blood  from  animals  in- 
jected with  diphtheria  antitoxin,  or  with  antitetanolysin. 

1  Morgenroth  and  Sachs:  Berl.  klin.  Wochenschrift,  No.  35,  p.  8  (1902). 

2  Bashford:  Journ.  of  Pathology  and  Bacteriology,  9.  192  (1903). 


246  LECTURES  ON  IMMUNITY 

The  experiments  do  not  succeed  if  the  passively  immunised 
animal  is  of  the  same  species  as  that  which  has  produced 
the  antitoxin. 

Probably  the  new  antibody,  the  anti-antiricin,  binds  the 
antiricin,  just  as  ricin  does,  so  that  the  antiricin  becomes 
divided  between  the  ricin  and  the  antibody ;  and  therefore 
the  ricin  acts  as  if  a  less  quantity  of  antiricin  than  that  used 
in  the  experiment  had  been  employed. 

In  the  same  manner  it  is  possible  by  intravenous  injec- 
tion of  a  haemolysin  (i.e.  an  antierythrocytic  substance)  to 
produce  corresponding  antibodies.  Thus,  for  instance, 
after  the  injection  of  immune-body  from  the  blood-serum 
from  a  rabbit  which  had  been  actively  immunised  against 
bovine  erythrocytes  into  the  veins  of  a  guinea-pig,  this 
animal  presented  in  its  serum  an  anti-immune-body,  specific 
against  the  injected  immune-body.  Such  experiments 
were  first  carried  out  by  Bordet,1  who  called  the  new 
antibody  "  anti-sensibilisatrice."  Nearly  simultaneously 
Ehrlich  and  Morgenroth2  produced  what  they  called 
"anti-immune-bodies,"  and  later  on  " anti-amboceptors." 
Pfeiffer  and  Friedberger3  prepared  anti-immune-bodies 
against  cholera-serum  from  a  goat,  by  injecting  such 
serum  into  the  veins  of  a  rabbit. 

Now,  a  compound  haemolysin  contains  immune-body 
and  alexin  and  hasmolysin  ;  it  may  therefore  seem  possible 
to  obtain  antibodies  against  these  three  different  sub- 
stances. To  determine  if  the  antibody  be  anti-immune- 


1  Bordet:  Ann.  de  VInst.  Pasteur,  14,  270  (1900). 

2  Ehrlich  and  Morgenroth:   Berl.  klin.    Wochenschrift,   No.  31   (1900); 
Nos.  21  and  22  (1901). 

8  Pfeiffer  and  Friedberger  :  Berl.  klin.  Wochenschrift,  No.  I  (1902). 


THE  COMPOUND   H^EMOLYSINS  247 

body  or  antialexin,  Ehrlich  and  Morgenroth  proceeded  in 
the  following  manner.  Immune-body  is  added  to  the  anti- 
body, and  if  this  is  an  antialexin,  it  leaves  the  immune-body 
free,  which  thereafter  may  be  extracted  with  erythrocytes, 
that  may  afterward  be  haemolysed  through  treatment  with 
alexin.  If  it  be  an  anti-immune-body,  it  binds  the  immune- 
body  present,  which  thereafter  cannot  be  extracted  by 
erythrocytes. 

Evidently  the  antihsemolysm,  if  such  an  antibody  exists, 
behaves  in  this  case  as  the  antialexin.  The  specificity  is 
not  very  prominent.  Normal  serum  contains  anti-immune- 
bodies  and  antialexins,  and  after  its  injection  into  animals 
these  produce  antialexins.  According  to  Ehrlich  and 
Morgenroth,  inactivated  serum  heated  to  56°  C.,  which 
ought  not  to  contain  alexin,  still  gives  an  antialexin  after 
injection.  (The  antialexins  resist  a  temperature  of  55- 
60°  C. ;  usually  they  are  heated  before  using  in  order 
to  free  them  of  perturbations  through  the  presence  of 
alexins.)  Another  peculiarity  was  found  by  Ehrlich  and 
Morgenroth,  namely,  that  serum  from  a  goat  previously 
injected  with  serum  from  a  rabbit  contains  an  antialexin, 
not  only  against  the  alexin  in  rabbit-serum,  but  also 
against  the  alexin  contained  in  guinea-pig-serum.  The 
same  antialexin  is  even  contained  in  the  serum  of  a  goat 
treated  by  injections  of  horse-serum. 

The  antialexins  have  been  regarded  as  especially  im- 
portant because  they  bind  the  alexins,  which  are  — 
according  to  the  views  of  Bordet  as  well  as  of  Ehrlich 
—  the  effective  parts  of  the  haemolysins.  Therefore  the 
chief  part  of  the  work  on  the  antihaemolytic  substances 
has  been  concerned  with  investigations  of  antialexins, 


248  LECTURES  ON  IMMUNITY 

which  were  generally  prepared  simply  by  the  injection  of 
the  normal  serum  of  one  animal  into  the  veins  of  another 
animal.  As  will  be  seen  from  the  following  accounts  of 
the  results  of  experiments,  the  sera  thus  prepared  seem 
to  contain  anti-immune-bodies  as  well  as  antialexins.1  And 
regarding  the  relative  probability  of  the  production  of 
these  two  antibodies,  it  must  be  said  that  as  the  immune- 
bodies  are  very  much  more  rare  than  the  alexins,  the 
organism  will  more  easily  produce  the  necessary  quantity 
of  anti-immune-bodies  than  of  antialexins.  Moreover,  the 
serum  of  the  animal  which  is  exposed  to  dangers  of  a 
haemolytic  nature  contains  in  its  blood-serum  generally 
an  alexin  which,  united  with  the  proper  immune-body, 
haemolyses  its  own  erythrocytes.  Against  this  alexin  the 
animal  evidently  produces  no  antibody,  for  otherwise 
the  alexin  would  be  of  no  use  against  foreign  substances 
which  enter  the  blood. 

Morgenroth  and  Sachs2  have  carried  out  an  investiga- 
tion on  the  quantities  of  antialexin  which  are  necessary 
to  completely  suppress  the  action  of  a  mixture  of  immune- 
body  and  alexin  which  is  just  able  to  produce  complete 
haemolysis  of  the  erythrocytes  used  in  the  experiment. 
The  results  are  given  in  the  following  table,  where  a 
denotes  the  quantity  of  immune-body  (given  as  number 
of  c.c.  of  the  preparation  used),  b  the  corresponding  quan- 
tity of  alexin,  and  c  the  quantity  of  antialexin  necessary 
to  inhibit  the  haemolysis.  The  erythrocytes  were  present 
in  the  amount  of  i  c.c.  of  a  five  per  cent  suspension.  The 
alexin  and  the  antialexin  were  in  contact  for  thirty  minutes 

1  This  circumstance  has  been  observed  already  by  Bordet  (I.e.  p.  273). 

2  Morgenroth  and  Sachs:  Berl.  klin.  Wochenschrift,  No.  35  (1902). 


THE  COMPOUND   H^MOLYSINS  249 

at  37°  C.  before  the  erythrocytes  and  the  immune-body 
were  added. 

EXPERIMENTS  OF  MORGENROTH  AND  SACHS  ON  ANTIALEXIN 

i.  SHEEP  BLOOD  ERYTHROCYTES 

Immune-body,  from  goat  treated  with  sheep  erythrocytes ;  alexin,  normal  serum  of 

guinea-pigs ;  antialexin,  immune-serum  from  goat,  treated  with  rabbit-serum 
a  6  c  c :  b  c  \  a. 

0.3  0.006  0.35  58  1.2 

0.05  0.006  O.I  17  2 

o.oi  o.oi  o-°75  7-5  7-5 

0.005  °-°5  0-015  °-3  I0 

2.  Like  I,  but  the  antialexin  is  from  a  rabbit  which  has  been  treated  with  guinea- 
pig-serum 

a.  b  c  c  :  b  c :  a 

0.2  0.0035  0.005  I-4  0.025 

o.i  0.025  °-°4  J-6  0.4 

3.  BOVINE  ERYTHROCYTES 

Immune-body,  from  rabbit  treated  with  bovine  erythrocytes;  alexin,  normal  serum 
of  guinea-pigs ;  antialexin,  from  goat,  treated  with  rabbit-serum 

a.  b  c  c:b  c  :  a 

0.2  0.05  0.75  15  38 

0.004  o-1  °-i  i.o  25 

4.  ERYTHROCYTES  FROM  HUMAN  BLOOD 

Immune-body,  from  a  rabbit,  treated  with  human  erythrocytes;   alexin,  normal 
serum  from  a  rabbit ;  antialexin,  from  goat,  treated  with  rabbit-serum 

a  b  c  c  '.  b  c '.  a 

0.2  0.05  0.075  x-5  °-38 

o.i  0.05  °-°35  °-7  0.35 

0.05  o.i  0.025  o>25  °-5 

Only  in  the  case  2  is  there  the  approximate  proportionality 
between  c  and  b  which  was  expected  by  the  authors.  Evi- 
dently if  the  alexin  is  bound  by  the  antialexin  without 
dissociation,  the  quantity  of  antialexin  necessary  for  neu- 
tralisation will  be  proportional  to  the  quantity  of  alexin 
used,  just  as  is  the  case  in  this  experiment.  The  authors 
call  attention  to  the  remarkable  fact  that  in  this  case  the 


250  LECTURES  ON   IMMUNITY 

antialexin  was  produced  by  the  injection  of  the  alexin 
used,  which  was  not  the  case  in  the  other  series.  It  seems 
quite  possible  that  this  method  is  the  only  one  adapted  to 
yield  a  specific  antialexin  with  a  strong  affinity  for  the 
injected  alexin. 

If  the  affinity  be  not  very  marked,  and  therefore  the 
reaction  between  alexin  and  antialexin  to  a  high  degree 
incomplete,  we  would  not  expect  to  find  a  proportionality 
between  the  neutralising  quantity  of  antialexin  and  the 
quantity  of  alexin  present.  (It  may  be  remarked  that  it 
is  here  not  a  question  of  an  absolute  neutralisation,  by 
which  the  quantity  of  haemolysin  would  sink  to  zero, 
but  only  of  a  reduction  of  the  quantity  of  haemolysin  to 
about  14  per  cent  of  the  value  exhibited  in  the  absence 
of  antialexin  (cf.  p.  229).) 

What  complicated  phenomena  may  be  encountered  in 
such  cases  is  evident  from  the  following  example,  in  which 
it  is  supposed  that  the  formula  valid  for  the  equilibrium 
has  the  form,  (5  a  —  ;r)(2O  b  —  x)—  100  x>  which  quite 
closely  corresponds  to  the  combination  of  the  immune-body 
(a)  from  a  goat  treated  with  bullock  erythrocytes  and  with 
guinea-pig  serum  as  alexin  (b)  to  haemolysin  (;r).  I  have 
supposed  that  an  antialexin  of  the  same  affinity  for  the 
alexin  as  that  of  the  immune-body  is  added,  so  that  the 
same  formula  may  be  used  for  the  two  cases  of  equilibrium. 
From  this  it  follows  that  the  proportions  of  alexin  bound 
to  immune-body  and  antialexin  are  identical  with  the  pro- 
portions of  these  two  substances  themselves.  The  fol- 
lowing table  corresponds  directly  to  those  of  Morgenroth 
and  Sachs,  b  is  the  quantity  of  alexin  necessary  for  com- 
plete haemolysis  in  the  presence  of  the  quantity  a  of  im- 


THE  COMPOUND   H^EMOLYSINS 


251 


mime-body,  c  is  the  quantity  of  antialexin  necessary  to 
reduce  the  quantity  of  haemolysin  to  the  eighth  part  of 
that  necessary  for  total  haemolysis,  which  nearly  corre- 
sponds to  the  limit  of  observable  haemolysis. 

INFLUENCE  OF  ANTIALEXIN  ACCORDING  TO  THE  LAW  OF  MASS-ACTION 


a 

b 

c 

C'.b 

c  :  a 

1000 

5-i 

7130 

1400 

7-i 

300 

5-4 

2270 

45° 

7.6 

100 

6-3 

885 

141 

8.9 

70 

7.0 

690 

99 

9-9 

50 

8.4 

606 

72 

12.  1 

30 

'5 

670 

45 

22-3 

25 

25 

95° 

38 

38.1 

Here  we  observe  that  for  a  certain  quantity  of  immune- 
body  (a  =40 ;  b  =  10),  when  the  immune-body  and  the  alexin 
are  present  in  equivalent  quantities,  c  passes  through  a 
minimum ;  for  higher  values  of  a,  c  increases  with  a  and 
tends  to  reach  proportionality  with  a  as  a  attains  very  high 
values;  for  lower  values  of  a,  c  increases  with  b.  In 
other  words,  the  addition  of  a  given  quantity  of  antialexin 
has  a  maximal  influence  when  a  —  40,  and  the  haemolytic 
action  is  reduced  to  a  lesser  degree  for  values  of  a  above 
or  below  40.  The  general  behaviour  will  be  the  same  even 
if  the  affinity  of  the  immune-body  for  the  alexin  is  not 
equal  to  that  of  the  antialexin  for  the  alexin,  only  then 
the  minimum  of  c  is  displaced. 

If  we  now  compare  this  last  general  table  with  those  of 
Sachs  and  Morgenroth,  we  observe  that  all  of  them  may 
very  easily,  within  the  errors  of  observation,  be  regarded 
as  special  cases  of  the  general  table ;  while  they  conclude 


252  LECTURES   ON  IMMUNITY 

that  from  their  observations  "  it  must  of  necessity  (!)  be 
concluded,  that  the  different  relations  of  the  affinities  can- 
not give  a  sufficient  explanation."  "We  must  therefore," 
they  say,  "  make  use  of  another  factor,  namely,  the  plu- 
rality of  the  alexins  and  antialexins,  for  the  explanation." 
This  conclusion  shows  clearly  how  necessary  it  is  to  be 
cautious  in  regard  to  theoretical  deductions  in  this  disci- 
pline of  bio-chemistry.  The  results  of  similar  deductions 
led  Bashf ord *  to  introduce  one  of  his  memoirs  with  the 
words:  "  On  immunity,  especially,  investigation  is  rendered 
difficult  by  the  habit  of  pushing  conclusions  farther  than 
the  facts  really  warrant;  impartial  work  and  judgment  too 
often  lead  to  the  conviction  that  the  '  generally  accepted 
facts '  are  but  flimsily  supported  hypotheses." 

The  relations  are  still  more  complicated  by  the  possi- 
bility that  the  velocity  of  absorption  for  immune-body  and 
antialexin  may  be  rather  different  in  different  cases. 

In  two  masterly  memoirs  Bordet2  has  considered  the 
properties  of  antisera,  procured  by  injection  of  normal  and 
immune  sera  into  the  veins  of  a  non-related  animal.  Bor- 
det found  that  serum  from  the  guinea-pigs  which  had  been 
treated  with  erythrocytes  from  a  rabbit  caused  after  injec- 
tion into  a  rabbit,  the  production  of  substances  which 
counteracted  the  immune-body  contained  in  the  immune- 
serum  of  guinea-pigs,  as  well  as  the  alexin  in  normal  serum 
from  guinea-pigs.  This  antialexic  action  not  only  protected 
the  erythrocytes  of  rabbit,  treated  with  the  said  immune- 
serum,  from  being  haemolysed,  but  even  cholera  vibrios, 

1  Bashford:  Journ.  of  Pathology  and  Bacteriology,  8.  52  (1902). 

2  Bordet :  Ann.  de  VInst.  Pasteur •,  18.  593  (1904) ;  Bordet  and  Gay :  ibidem, 
20.  467  (1906). 


THE  COMPOUND  H^IMOLYSINS  253 

treated  with  bacteriolytic  cholera-serum,  from  being  de- 
stroyed by  guinea-pig-serum.  This  antialexic  action  was 
in  so  far  specific  that  it  did  not  protect  against  other  alexins 
than  that  from  guinea-pigs.  Bordet  made  a  large  number 
of  experiments  with  the  following  combination :  erythro- 
cytes, from  bullock ;  immune-body,  serum  of  rabbit  injected 
with  erythrocytes  from  bullock ;  alexin,  normal  serum  from 
a  guinea-pig ;  antiserum,  serum  from  a  guinea-pig  treated 
with  normal  rabbit-serum.  The  immune-body  and  the 
antiserum  were  freed  of  alexin  by  heating  to  55-56°  C. 
for  thirty  minutes.  Bordet  separated  the  active  sub- 
stances from  a  large  number  of  other  substances  present 
in  the  sera  by  letting  the  erythrocytes  absorb  them,  then 
only  those  substances  that  were  specific  to  the  erythrocytes 
were  able  to  act.  That  the  erythrocytes  absorb  the  im- 
mune-body almost  completely  if  it  be  not  present  in  great 
excess,  we  have  seen  above;  and  this  method  has  long 
been  used  for  the  extraction  of  immune-bodies  from  sera. 
Bordet  has  shown  that  erythrocytes  charged  with  immune- 
body  also  absorb  alexins,  so  that  a  serum  may  in  this  way 
be  freed  from  its  content  of  alexin,  which  is  indicated  by 
the  fact  that  it  has  lost  its  hasmolytic  power  against  ery- 
throcytes treated  with  immune-body.  The  alexin  is,  on  the 
other  hand,  not  absorbed  by  normal  erythrocytes,  those 
that  do  not  contain  immune-body.  Further,  Bordet  in  an 
analogous  manner  proved  that  erythrocytes,  charged  with 
immune-body,  absorb  the  antiserum  and  thereafter  have 
lost  their  power  of  absorbing  alexin.  Evidently  the  im- 
mune-body is  neutralised  by  the  antiserum,  which  seems 
to  have  a  stronger  affinity  for  the  immune-body  than  has 
alexin.  This  observation  is  confirmed  by  the  fact  that  a 


254  LECTURES  ON  IMMUNITY 

certain  quantity  of  antiserum  can  bind  only  a  given  equiv- 
alent quantity  of  immune-body,  so  that  erythrocytes  pro- 
tected from  haemolysis  by  the  absorption  of  a  certain 
quantity  of  antiserum  may  yet  be  haemolysed  on  the  further 
addition  of  immune-body  and  alexin.  Normal  rabbit-serum 
heated  to  56°  C.  contains  a  substance  which  does  not  act  as 
an  immune-body  against  bovine  erythrocytes,  but  has  the 
faculty  of  binding  antiserum,  so  that  it  can  produce  the 
haemolysis  of  erythrocytes  that  are  loaded  with  the  com- 
pound of  immune-body  and  antiserum.  This  haemolytic 
action  is  weaker  if  the  compound  has  lain  for  a  long  time 
in  the  erythrocytes,  than  if  the  preparation  is  fresh.  This 
peculiarity  seems  to  indicate  that  the  compound,  just  as  the 
analogous  haemolytic  substances  such  as  tetanolysin  and 
probably  also  the  compound  hoemolysins,  is  slowly  bound 
by  the  protein  substances  in  the  erythrocytes.  The  normal 
rabbit  serum  evidently  contains  some  substance  which  com- 
petes with  the  immune-body  in  binding  antiserum. 

Bordet  and  Gay  made  an  observation  confirming  a  dis- 
covery of  Klein.1  The  immune-bodies  and  alexins  con- 
tained in  sera  are  absorbed  to  a  much  higher  degree  by  the 
erythrocrytes  if  these  are  suspended  in  a  physiological 
salt-solution,  than  if  they  are  suspended  in  a  natural  serum. 
Thus  a  mixture  of  0.4  c.c.  of  normal  horse-serum  and 
0.4  c.c.  of  erythrocytes  from  the  guinea-pig  was  treated 
with  i  c.c.  of  ox-serum  without  showing  agglutination  of 
the  erythrocytes  to  a  notable  degree.  If,  on  the  other  hand, 
0.6  c.c.  of  physiological  salt-solution  had  been  present  for 
some  time  in  the  said  mixture,  agglutination  was  very 
pronounced.  In  an  analogous  manner  we  may  explain  an- 

1  Klein:  Wientr  klin.  Wochcnschrift,  No.  48  (1905). 


THE  COMPOUND   H^MOLYSINS  255 

other  observation  of  Bordet.  0.2  c.c.  of  bovine  erythrocytes 
loaded  with  immune-body  were  mixed  with  0.6  c.c.  of 
antiserum  and  physiological  salt-solution.  After  a  time  the 
erythrocytes  were  separated  from  the  liquid  by  centrif ugal- 
isation.  To  the  erythrocytes  was  then  added  a  mixture  of 
0.2  c.c.  of  alexin  from  the  guinea-pig  with  0.6  c.c.  of 
normal  guinea-pig-serum  heated  to  56°  C.  Another  ex- 
periment was  quite  similar,  but  instead  of  the  O.6  c.c.  of 
guinea-pig-serum,  0.6  c.c.  of  physiological  salt-solution 
was  added.  In  the  first  experiment  no  haemolysis  was 
observed,  but  the  second  gave  haemolysis  during  the  course 
of  one  hour.  The  absorption  of  the  alexin  was  much 
greater  in  the  presence  of  the  physiological  salt-solution 
than  in  the  presence  of  normal  serum.  The  absorbed 
alexin  competes  with  the  antiserum  absorbed  in  the  erythro- 
cytes, so  that  a  certain  quantity  of  compound  haemolysin 
was  formed,  enough  to  yield  haemolysis. 

This  action  of  the  physiological  salt-solution  which 
causes  the  absorption  of,  e.g.,  the  immune-body  and  the 
alexin  from  horse-serum  in  the  experiment  of  Bordet  and 
Gay,  speaks  very  much  in  favour  of  the  view  that  an  ab- 
sorption and  not  a  chemical  binding  of  the  immune-bodies 
takes  place  in  the  erythrocytes. 

Through  absorption  experiments  Bordet  proved  that  the 
same  antiserum  protects  bovine  erythrocytes  against  the 
immune-body  contained  in  serum  from  a  rabbit  treated  with 
bovine  erythrocytes,  and  chicken  erythrocytes  against  rab- 
bit-serum treated  with  chicken  erythrocytes.  The  same 
antiserum  may  therefore  neutralise  two  entirely  different 
immune-bodies,  which  are  produced  by  the  same  species 
of  animal  (here  rabbits).  Therefore  Bordet  rejects  the 


256  LECTURES  ON   IMMUNITY 

proof  given  by  Ford  and  Wassermann,1  that  the  agglutinin 
to  chicken  erythrocytes,  which  is  found  in  normal  rabbit- 
serum,  is  identical  with  that  contained  in  serum  from  rab- 
bits treated  with  the  said  erythrocytes,  because  both  are 
neutralised  by  serum  from  chicken  treated  with  rabbit 
erythrocytes. 

Bordet  makes  some  remarks  of  great  theoretical  interest 
bearing  upon  the  results  of  his  experiments.  Ehrlich  and 
Morgenroth2  found  that  in  the  said  combination  of  erythro- 
cytes and  immune-body  it  was  possible  to  use  alexin  from 
goat-serum,  although  it  had  a  weaker  haemolytic  action 
than  that  from  guinea-pigs.  They  then  made  experiments 
with  the  neutralising  action  of  an  antiserum  produced  by 
the  injection  of  serum  from  rabbits  treated  with  bovine 
erythrocytes  into  the  veins  of  a  goat.  They  found  that  this 
serum  (in  a  given  quantity)  hindered  the  haemolysis  by 
alexins  from  guinea-pigs,  but  not  by  that  of  goat-serum. 
But  as  the  alexin  from  goats  is  much  weaker,  they  used  in 
this  special  case  a  much  greater  quantity  of  immune-body. 
Thereby  they  introduced  not  alone  the  immune-body  in 
great  quantity,  but  also  the  substances  contained  in  normal 
rabbit-serum  which  are  able  to  neutralise  the  antiserum. 
Bordet  explains  in  this  simple  manner  that  the  antiserum 
Jhad  no  action  in  this  case,  and  rejects  the  explanation  of 
Ehrlich  and  Morgenroth,  who  assume  that  the  different 
effect  is  due  to  the  presence  of  two  different  kinds  of  im- 
mune-bodies in  the  preparation,  of  which  the  one  gives 
compounds  with  the  alexin  from  guinea-pigs  and  with  the 

JFord:  Zeitschr.  f.  Hygiene,  40.  363  (1902);  Wassermann:  ibidem,  42. 
267  (1903). 

2  Ehrlich  and  Morgenroth:  Berl.  klin.  Wochenschrift,  Nos.  21  and  22 
(1901). 


THE  COMPOUND   H^MOLYSINS  257 

antiserum,  the  other  with  alexin  from  goats  but  not  with 
the  antiserum  used.  Evidently  this  proof  is  without 
validity.  This  is  now  conceded  by  Ehrlich,  who  believes, 
however,  that  other  proofs  are  still  valid.1 

Another  remark  of  Bordet  touches  the  side-chain  theory 
of  Ehrlich.  Ehrlich  conceives  the  formation  of  antibodies 
in  the  following  manner :  If  a  foreign  substance  is  injected 
into  the  body  of  an  animal,  it  may  be  "  anchored  "  to  some 
cells  in  the  tissues  of  the  animal.  A  chemical  affinity 
localised  on  a  "  receptor  "  of  this  cell  is  thereafter  bound, 
and  hence  the  cell  is  hindered  in  one  of  its  functions.  The 
cell  then  produces  a  new  "receptor"  to  fill  the  place  of 
that  seized  by  the  foreign  substance.  "  According  to  a  law 
of  Weigert's,  the  regeneration  does  not  only  compensate 
the  defect,  but  overcompensates  it."  (This  so-called 
"  law"  has  no  standing  whatever.)  The  excess  of  recep- 
tors thus  produced  is  given  off  to  the  blood  and  forms 
the  antitoxin.  In  our  case,  therefore,  the  immune-body, 
according  to  Ehrlich,  is  a  receptor  which  is  able  to  bind 
an  erythrocyte.  This  receptor  is  called  amboceptor,  be- 
cause it  may  even  bind  a  molecule  of  alexin  at  the 
same  time  as  the  erythrocyte.  Now,  we  have  seen  that 
the  immune-bodies  are  probably  not  bound  by  the  erythro- 
cytes,  but  only  absorbed  by  them.  Therefore,  in  its  old 
formulation,  the  side-chain  theory  probably  has  no  appli- 
cation to  this  special  case.  Bordet,  on  the  other  hand, 
accepts  the  theory  of  a  binding  process  like  that  by  which 
dyes  are  bound  to  fibre.  He,  therefore,  seeks  another 
proof  that  the  theory  of  Ehrlich,  as  it  is  used,  cannot  be 
correct.  To  explain  the  action  of  antisera  Morgenroth 

1  Ehrlich  and  Sachs:  Berl  klin.  Wochenschrift>  Nos.  19  and  20  (1905). 
s 


LECTURES  ON  IMMUNITY 

supposes  that  they,  as  formed  by  the  injection  of  an  im- 
mune-body, consist  of  receptors  which  bind  the  same 
affinity  of  the  immune-body  that  otherwise  might  bind  the 
erythrocyte.  (Evidently  it  would  be  much  better  to  sup- 
pose, as  Ehrlich  does  in  his  reply  to  Bordet,  that  the 
antisera  may  replace  the  alexins,  and  therefore  do  not 
attack  the  affinity  with  which  an  erythrocyte  may  be 
bound.)  Then,  Bordet  retorts,  every  substance  capable 
of  binding  the  antiserum  ought  to  bind  erythrocytes. 
As  we  have  seen,  normal  rabbit-serum  contains  a  sub- 
stance which  combines  with  the  antiserum,  but  not  with 
bovine  erythrocytes.  Even  immune-serum  from  the  rabbit 
treated  with  bovine  erythrocytes,  which  serum  had  pre- 
viously, by  being  shaken  with  ox  erythrocytes,  been  de- 
prived of  substances  that  bind  these  erythrocytes,  showed 
an  affinity  for  antiserum.  Further,  the  same  antiserum 
binds  immune-bodies  which  are  absorbed  by  different 
erythrocytes,  as  bullock's  and  hen's,  and  which  are  specific 
for  them. 

Hence  the  attack  of  Bordet  on  the  side-chain  theory  in 
the  form  of  its  original  application  to  this  phenomenon  was 
quite  correct.  But  this  theory  possesses  a  high  degree  of 
elasticity,  and  against  the  new  formulation  given  by 
Ehrlich  and  Sachs  in  their  reply  to  Bordet,  according  to 
which  the  antiserum  competes  with  the  alexin  in  binding 
the  immune-body,  no  objection  is  to  be  made. 

We  might,  perhaps,  therefore  look  for  a  new  method  of 
elucidation  of  this  theoretical  question.  But,  as  Bordet 
remarks,  Ehrlich  has,  in  his  later  publications,  modified 
the  side-chain  theory  to  such  a  degree  that  the  differences 
between  Bordet's  and  Ehrlich's  opinions  almost  disappear, 


THE  COMPOUND  H^EMOLYSINS  259 

and  are  now  more  of  a  formal  than  of  a  real  character. 
Evidently,  if  an  animal  reacts  to  injection  of  a  foreign  fluid 
substance,  the  simplest  way  to  explain  this  is  to  assume 
that  the  injected  fluid  attacks  some  cell  of  the  animal 
chemically.  In  common  language,  we  say  that  some  sub- 
stance in  the  fluid  has  been  bound  by  the  cells.  The  ani- 
mal retaliates  with  the  production  of  some  substance,  the 
so-called  antibody,  which,  as  we  have  seen,  partially  binds 
the  reacting  substance  in  the  fluid ;  if  the  reacting  substance 
be  a  cell,  the  antibody  enters  into  similar  cells,  and  in  many 
cases  causes  chemical  alterations  in  the  contents.  As  now 
the  reacting  substance  is  bound  chemically  by  the  cells  of 
the  inoculated  animal,  as  well  as  by  the  antibody  produced 
by  it,  we  may,  with  Ehrlich,  for  the  sake  of  simplicity,  sup- 
pose that  the  antibody  consists  of  just  that  part  of  the  cells 
which  are  attacked  by  the  foreign  fluid.  But  it  is  not 
necessary  to  make  this  supposition.  On  a  closer  inspec- 
tion, the  side-chain  theory  seems  to  be  little  more  than 
a  circumscription  of  the  definition  of  the  conception  "  anti- 
body," under  the  further  supposition  that  we  are  dealing 
with  chemical  processes.  If,  as  for  the  immune-bodies, 
no  proof  has  been  given  of  their  chemical  action,  the  side- 
chain  theory  finds,  in  its  present  state,  no  application. 

Bordet  also  makes  an  attack  upon  Morgenroth's l  proof 
that  immune-body  and  alexin  bind  each  other  in  solutions 
containing  both.  As  Morgenroth,2  and  likewise  Ehrlich 
and  Sachs,3  have  later  on  conceded  that  the  criticism  of 
Bordet  is  well  founded,  we  will  not  here  enter  upon  this 

1  Morgenroth:    Centralbl.f.  Baktcriologie,  35.  501  (1904). 

2  Morgenroth :   Arbeiten  aus  dem  pathologischen  Institut  zu  Berlin,  p.  6 
(1906). 

8  Ehrlich  and  Sachs :  /.<:.,  p.  1 6. 


260  LECTURES  ON  IMMUNITY 

criticism.  We  only  remark  that  the  compound  is  very 
easily  dissociated,  so  that  it  was  only  with  the  help  of 
quantitative  measurements  that  a  proof  of  its  presence 
could  be  given  (cf.  p.  224).  As  this  compound  occurs  in 
the  erythrocytes,  it  would  seem  very  improbable  that  it 
should  not  exist  also  outside  of  the  erythrocytes,  although 
dissociated  to  a  high  degree. 

As  we  have  seen  above,  Ehrlich  and  Sachs  made  experi- 
ments with  erythrocytes  from  guinea-pigs,  normal  bovine 
serum  heated  to  56°  C.  (which  they  regarded  as  immune- 
body),  and  alexin  from  horse  blood.  They  found  that  the 
haemolytic  agent  from  the  bovine  serum  was  not  absorbed 
by  the  erythrocytes,  for  it  did  not  lose  its  activity  after 
having  been  shaken  with  such  erythrocytes.  Hence  they 
concluded  that  not  the  immune-body,  but  its  compound 
with  alexin,  is  absorbed  by  the  erythrocytes.  This  con- 
clusion is  not  corroborated  by  the  investigation  of  Bordet 
and  Gay,  for  they  found  that  if  they  used  alexin  from 
guinea-pigs  instead  of  alexin  from  horses,  haemolysis  oc- 
curred, but  not  after  the  immune-body  had  been  separated 
from  the  bovine  serum  by  treatment  with  erythrocytes 
from  guinea-pigs.  There  must  therefore  be  another  ex- 
planation of  the  experiments  of  Ehrlich  and  Sachs.  After 
a  thorough  investigation,  Bordet  and  Gay  conclude  that 
the  normal  horse-serum,  used  by  Ehrlich  and  Sachs, 
furnishes  not  only  the  alexin,  but  also  the  immune- 
body  to  the  erythrocytes.  The  compound  haemolysin 
of  these  two  substances  is  too  weak  to  cause  a  percep- 
tible haemolysis,  but  it  is  strengthened  by  the  presence 
of  some  substance  contained  in  the  bovine  serum,  which 
they  call  "colloide  de  boeuf."  This  colloid  is  indeed 


THE  COMPOUND  H^EMOLYSINS 


26l 


active  in  other  similar  cases.  The  proof  of  Ehrlich 
and  Sachs  that  an  immune-body  is  not  itself  soluble  in 
(able  to  be  bound  by)  ery throcytes,  but  only  after  combina- 
tion with  alexin,  is  henceforth  untenable. 

I  have  made  some  experiments  on  the  action  of  anti- 
alexins  and  found  that  cases  occur  in  which  the  influ- 
ence of  the  antialexin  has  even  a  minimum  value  for  a 
medium  concentration  of  the  immune-body,  and  not  a  maxi- 
mum, as  in  the  theoretical  example  cited  above.  In  one 
case  the  erythrocytes  were  from  sheep  (i  c.c.  of  a 
5  per  cent  suspension) ;  the  immune-body  (a),  from  a  goat, 
treated  with  erythrocytes  from  sheep  the  alexin  (b)  was 
guinea-pig-serum ;  and  the  antialexin  (c)  was  from  a  goat 
injected  with  serum  from  a  rabbit.  The  quantity  of  alexin 
was  of  such  a  magnitude  that  three-fourths  of  it  would 
be  just  sufficient  to  produce  complete  haemolysis.  The 
quantities  are  given  in  centimetres  of  the  preparations  used. 
The  experimental  method  was  the  same  as  that  used  by 

ACTION  OF  DIFFERENT  QUANTITIES  OF  ANTIALEXIN 


SER.  i 

SER.  2 

SER.  3 

SER.  4 

c  (c.c.) 

a  =  0.1  c.c. 
£  =  0.004  c  c- 

«=O.OI  C.C. 

b  =0.015  c.c. 

a  =  0.001  c.c. 
£  =  0.04  c.c. 

«  =  0.0005  c.c. 

3=0.1  C.C. 

0 

IOO 

IOO 

IOO 

IOO 

0.025 

67 

IOO 

IOO 

IOO 

0.035 

48 

IOO 

IOO 

90 

0.05 

22 

IOO 

IOO 

Si 

0.075 

H 

IOO 

54 

36 

O.I 

9 

90 

4(?) 

13 

0.15 

6 

28 

4 

8 

0.25 

8 

12 

6 

8 

0-35 

8 

7 

6 

9 

o-5 

10 

8 

8 

9 

262  LECTURES  ON  IMMUNITY 

Morgenroth  and  Sachs.  The  total  quantity  was  2.2  c.c. 
The  tabulated  quantity  is  the  degree  of  haemolysis. 

The  action  is  the  least  in  Ser.  2,  after  this  comes  Ser.  3, 
then  Ser.  4,  and  last  Ser.  I.  It  seems  difficult  to  explain 
this  peculiar  behaviour,  which  was  controlled  by  other 
measurements,  so  long  as  we  suppose  that  the  "antialexin" 
entered  into  combination  only  with  the  alexin  present. 
The  observations  may  be  understood  if  we  assume  that 
either  an  anti-immune-body  or  an  antihaemolysin  was  pres- 
ent. If  we  suppose  that  the  preparation  c  contained  anti- 
immune-body  as  well  as  antialexin  and  their  affinities  are 
strong,  then  small  quantities  of  c  may  be  sufficient  for  the 
neutralisation  to  a  remarkable  degree  if  small  quantities  of 
either  the  alexin  (Ser.  i)  or  of  the  immune-body  (Ser.  4) 
are  present.  The  explanation  is  analogous  (the  result 
of  the  partial  dissociation)  if  we  suppose  the  presence  of 
an  antihaemolysin  in  the  solution  c. 

In  any  case  the  reactions  in  the  presence  of  antialexins 
or  anti-immune-bodies  are  rather  complicated  and  difficult 
of  survey. 


CHAPTER   IX 
THE  PRECIPITINS   AND  THEIR  ANTIBODIES 

IN  many  instances  the  reaction-products  of  the  ferments 
are  solid  bodies,  and  such  ferments  are  called  precipitins. 
Generally  these  solid  substances  contain  a  great  deal  of 
water,  like  albuminous  substances  in  general ;  and  this  cir- 
cumstance has  in  recent  times  led  to  the  opinion  that  the 
act  of  precipitation  might  consist  only  of  a  coalescence  and 
subsidence  of  the  "colloidal"  particles  of  the  particular 
albuminous  substance  in  the  system.  Thus,  for  instance, 
the  casein  of  milk  is,  according  to  this  theory,  present  in 
the  state  of  so-called  pseudo-solution.  Its  smallest  parti- 
cles may  be  regarded  as  an  extremely  fine  solid  powder  of 
ultramicroscopic  magnitude  (dimensions  less  than  .0002 
millimeter).  On  the  addition  of  rennet  these  solid  particles 
coalesce  to  form  larger  clumps  and  subside,  just  as  finely 
powdered  clay  sedimentates  following  the  addition  of  salts 
or  acids  to  the  water  in  which  it  is  suspended. 

In  corroboration  of  this  view  Duclaux l  cites  the  follow- 
ing observation.  "In  milk,  which  is  turning  sour  but 
which  is  still  quite  liquid,  we  observe  with  the  miscroscope, 
as  I  have  indicated,  a  precipitate  of  fine  grains,  which  at  the 
beginning  are  seen  only  with  difficulty,  and  are  detected 
only  by  a  faint  disturbance  of  the  visional  field,  but 
which  later  on  display  quite  distinct  granulations,  charac- 
terised by  the  Brownian  movement,  just  as  minute  particles 

1  Duclaux:  Microbiologief1omQ  2,  pp.  253-339  (1899). 
263 


264  LECTURES  ON  IMMUNITY 

of  clay.  Shall  we  suppose  now  that  the  coagulation  of  the 
casein  changes  its  value  rapidly  in  the  same  moment  that 
we  are  able  to  observe  its  progress  ?  From  this  point  of 
view  the  phenomenon  manifests  itself  to  our  eyes  as  a 
steadily  increasing  molecular  condensation.  It  displays  the 
behaviour  of  clay  particles  which  aggregate  and  subside. 
.  .  .  We  are  therefore  led  to  suppose  that  this  regular  con- 
densation, which  causes  the  coagulation  as  far  as  we  are 
able  to  observe  it,  begins  already  before  the  microscope 
can  detect  it.  But  however  well  grounded  this  induction 
may  seem  to  us,  it  would  remain  unfounded  if  we  could  not 
control  it  by  experiment." 

This  experimental  proof  Duclaux  finds  in  the  reaction 
of  Tyndall.  Ultramicroscopical  powders  suspended  in  an 
absolutely  clear  fluid  reveal  their  presence  by  the  produc- 
tion of  a  blue  colour  on  illumination  by  a  ray  of  light,  and 
this  blue  reflected  light  is  polarised.  This  phenomenon 
is  displayed,  for  instance,  by  a  suspension  of  fine  particles 
of  mastic,  prepared  by  adding  a  few  drops  of  an  alcoholic 
solution  of  mastic  to  water.  If  we  add  greater  quantities 
of  the  solution,  the  light  reflected  becomes  more  .pale  and 
white;  and  at  a  certain  point  it  is  possible  by  means  of  the 
microscope  to  detect  in  it  small  particles  that  show  the 
Brownian  movement.  At  a  still  higher  concentration  of 
the  solution  a  real  precipitate  is  formed,  which  is  easily 
observed  with  the  naked  eye. 

To  this  argument  may  be  added  still  another  fact.  Such 
submicroscopic  particles  may  be  observed  by  means  of 
the  ultramicroscope  of  Siedentopf.  Solutions  of  proteins 
generally  reveal  the  presence  of  such  submicroscopic 
granules,  and  this  observation  has  been  interpreted  in 


THE  PRECIPITINS  AND  THEIR  ANTIBODIES  265 

favour  of  the  view  that  all  solutions  of  proteins  may  be 
regarded  as  pseudo-solutions,  i.e.  consisting  of  suspensions 
of  finely  divided  particles.  Against  this  view  it  may,  how- 
ever, be  urged  that  the  presence  of  some  submicroscopic 
particles  does  not  prove  at  all  that  the  whole  of  the  quan- 
tity of  protein  present,  or  even  that  a  considerable  part  of 
it,  is  in  this  state  of  pseudo-solution. 

Even  in  this  case  some  salts,  especially  those  of  calcium, 
strontium,  and  barium,  exert  a  great  influence,  just  as  in 
the  case  of  agglutination,  with  which  the  phenomenon  of 
coagulation  shows  many  analogies.  (Cf.  above,  pp.  73  and 
159.)  Just  as  salts  are  of  marked  influence  on  the  agglom- 
eration of  fine  particles,  as,  e.g.,  of  clay  or  of  mastic  (cf.  p. 
1 59),  so  in  the  same  way  the  influence  of  the  salts  of  Ca, 
Sr,  and  Ba  on  the  process  of  coagulation  is  so  prominent 
that  it  is  doubtful  if  coagulation  can  be  realised  in  their 
absence.  These  salts  alone,  without  rennet,  give  precipi- 
tates with  milk  or  solutions  of  casein.  The  coagulated 
matter  is  more  flocculent  and  does  not  entangle  the  fat- 
drops  to  so  high  a  degree  as  the  coagulum  produced  under 
the  action  of  rennet.  But  this  action  of  the  salts  of  the 
metals  of  the  calcium  group  seems  to  be  rather  specific. 
Next  to  them  come  the  salts  of  magnesia,  which  accelerate 
also  the  coagulation  by  rennet  if  they  are  present  in  greater 
quantity,  though  according  to  Lorcher's  observations  small 
quantities  of  MgCl2  retard  the  action  of  rennet,  whereas 
even  the  least  traces  of  Ca,  Sr,  or  Ba  salts  accelerate  the 
coagulation  by  rennet.  These  salts  give  without  ren- 
net a  coagulation  with  the  casein  of  milk.  Salts  of  the 
other  alkali  metals  coagulate  milk  only  at  high  concentra- 
tions ;  they  retard  the  coagulating  action  of  rennet.  In 


266  LECTURES  ON  IMMUNITY 

strong  solution  even  the  salts  of  Ca,  Sr,  and  Ba  retard 
the  action  of  rennet.  This  action  of  stronger  solutions 
is  probably  only  due  to  a  change  in  the  solubility,  just 
as  the  precipitation  of  casein  by  means  of  alcohol,  and 
possesses,  therefore,  only  a  secondary  interest. 

Acids  precipitate  the  casein,  even  in  rather  minute  quan- 
tity. Salts  which  have  an  acid  reaction  accelerate  the 
action  of  rennet  just  as  acids  do.  This  may  be  due  to 
the  presence  of  free  acid  in  these  solutions.  On  the  other 
hand,  alkalies  hinder  or  retard  the  precipitation  of  the 
casein,  and  in  the  same  manner  behave  salts  with  an  alka- 
line reaction,  as  the  carbonates  or  bicarbonates  of  the  alkali 
metals.  These  last  facts  speak  very  much  in  favour  of 
the  chemical  theory  first  advanced  by  Hammarsten,  who 
regards  the  casein  as  an  acid,  which  is  very  slightly  solu- 
ble, whereas  its  salts  with  alkali  metals  are  soluble  in  water. 

Laqueur  and  Sackur1  have  determined  its  equivalent 
weight  to  be  1135.  The  conductivity  of  the  sodium  salt 
in  solution  seems  to  indicate,  according  to  a  rule  of  Ost- 
wald,  that  the  acid  is  tetra-  or  hexavalent,  so  that  its 
molecular  weight  is  computed  to  be  4540  or  6710. 

With  this  last  number  agrees  very  well  another  (6600), 
found  by  Hedin,  Blum,  and  Vaubel2  from  a  study  of  the 
products  of  the  decomposition  of  casein. 

By  the  prolonged  action  of  weakly  alkaline  solutions  on 
casein,  another  stronger  acid  is  formed,  termed  isocasein, 
possessing  the  equivalent  weight  960.  Its  molecular 
weight  is  four  or  six  times  greater. 

1  Laqueur  and  Sackur :  Hofmeisters  Beitrdge,  3  (1902);  Sackur:  Zeitschr.f. 
ph.  Ch.,  41.  672  (1902). 

2  Hedin,  Blum,  and  Vaubel:  Journ.  /. praktischc  CA.,  60.  55  (1899). 


THE   PRECIPITINS  AND  THEIR  ANTIBODIES  267 

Upon  these  chemical  properties  Hammarsten  founded 
his  method  for  the  preparation  of  pure  casein.  Milk  is  di- 
luted with  three  to  four  times  its  volume  of  water,  and  a  pre- 
cipitate produced  by  the  addition  of  o.  i  per  cent  of  acetic 
acid.  The  precipitate  is  separated  from  the  solution  by 
filtration  through  linen  and  then  dissolved  in  a  weak  solu- 
tion of  caustic  soda  or  better  ammonia.  The  fat-drops 
carried  down  by  the  precipitate  separate  upon  the  top  of 
the  liquid,  which  is  thereafter  again  precipitated  and  redis- 
solved  four  or  five  times.  The  last  traces  of  fat  are 
removed  from  the  precipitate  by  extraction  with  alcohol 
and  ether,  and  the  precipitate  is  after  that  dried  to  a  white 
powder,  casein,  which  is  very  slightly  soluble  in  water.  Its 
suspensions  in  water  behave  as  an  acid,  and  it  drives  the 
carbonic  acid  out  from  the  carbonates  of  alkali  metals  or 
calcium,  giving  clear  solutions  of  its  salts  with  these  metals. 

If  a  solution  of  the  calcium  caseate  is  neutralised  by 
the  addition  of  a  diluted  solution  of  phosphoric  acid,  a 
precipitate  of  calcium  phosphate  is  formed,  and  a  white 
liquid  remains  which  resembles  very  much  a  milk  devoid 
of  cream.  Probably  we  have  here  a  pseudo-solution  of 
casein.  It  behaves  like  milk  in  being  coagulated  through 
the  action  of  rennet. 

The  adherents  of  the  chemical  theory  of  coagulation  by 
rennet  assume  that  this  ferment  exerts  a  decomposing 
action  on  the  casein,  just  as  pepsin  on  protein,1  after  which 

1  According  to  recent  investigations  of  Bang  (Zeitschr.  f.  ph.  Ch.,  43.  358, 
1905),  Hemmeter  (Berl.  klin.  Wochenschrift,  E-wald-Nummer,  14,  1905), 
and  Schmidt -Nielsen  (Zeitschr.  f.  physiol  C/z.,  48.  92,  1906),  pepsin  and 
chymosin  —  the  milk-coagulating  substance  in  neutral  rennet  —  are  different 
substances.  Pepsin  seems  to  coagulate  milk  in  acid  solution,  wherein  the 
results  of  Pawlow  and  Sawjalow  find  their  explanation  (cf.  p.  71). 


268  LECTURES  ON  IMMUNITY 

the  digestion-product  is  precipitated  by  Ca  ions.  Some 
very  strong  arguments  are  advanced  in  favour  of  this  view. 
The  reaction  goes  on  at  low  temperatures  without  coagula- 
tion, which  then  occurs  almost  instantaneously  upon  eleva- 
tion of  the  temperature  to  over  25°  C.,1  and  small  quantities 
of  pepton  have  a  strong  retarding  influence  (cf.  p.  77).  One 
of  the  products  of  decomposition,  called  para-casein,  is  sup- 
posed to  yield  the  coagulum  at  higher  temperature,  whereas 
other  products,  for  instance  serum-albumen,  remain  in  solu- 
tion. In  reality  Hammarsten  has  proved  that  serum-albumen 
is  an  albumos-like  substance  with  characteristic  reactions :  it 
is  not  precipitated  by  acids  (acetic  and  nitric)  nor  by 
diluted  solutions  of  CuSO4,  HgCl2,  FeCl3,  K4(CN)6Fe,  nor 
Pb  (CH3CO2)2  J  it  does  not  give  the  reaction  of  Heller ;  but 
responds  to  the  biuret-reaction  and  the  reaction  of  Millon ; 
it  is  precipitated  by  tannin  in  acetic  acid  and  by  alcohol. 
Rennet  and  casein  produce  serum-albumen  even  in  absence 
of  calcium  or  barium  salts.  Duclaux  combats  this  view, 
which  he  says  leads  to  the  conclusion  that  these  soluble 
products  ought  to  pass  through  a  Chamberland  filter. 
Now  a  Chamberland  filter  restrains  casein,  but  some  of  the 
proteins  of  milk  pass  through  it.  Therefore,  according  to 
Duclaux,  milk  filtered  through  a  Chamberland  filter  should 
give  a  filtrate  containing  more  of  the  filterable  proteids 
after  it  had  been  coagulated  by  rennet,  than  before  this 
treatment.  This,  he  showed,  was  not  the  case.  But  the 
conclusion  drawn  does  not  seem  to  be  quite  convincing. 
For,  just  as  the  casein  does  not  pass  through  the  filter,  so 
the  serum-albumen  may  be  held  back  by  it.  That  the 


lrThis  was  first  observed  by  Morgenroth   (Archives   Internationales  dt 
pharmacodynamie^  7.  265,  1900). 


THE  PRECIPITINS  AND  THEIR  ANTIBODIES  269 

casein  does  not  pass  through  is  explained  by  Duclaux  as 
due  to  its  state  of  pseudo-solution,  which  is  really  only  a 
mode  of  expression  and  no  real  explanation ;  and  the  same 
property  may  be  characteristic  of  the  serum-albumen, 
especially  if  the  filter  is  covered  by  a  gel  of  casein. 

The  addition  of  a  solution  of  an  oxalate  or  of  a  fluoride 
to  milk  inhibits  its  coagulation.  One  might  suppose  this 
action  to  be  due  to  the  precipitation  of  the  calcium  from 
the  compounds  of  the  milk  and  of  the  rennet.  Duclaux 
combats  this  view  and  states  that  the  coagulation  is  not 
inhibited  if  the  oxalate  (or  fluoride)  is  not  present  in  excess. 
He  assumes  that  the  oxalate  or  fluoride  has  itself  a  direct 
influence  upon  the  milk,  lowering  its  tendency  to  coagula- 
tion. From  the  modern  point  of  view  of  physical  chemistry, 
it  seems  quite  obvious  that  for  the  coagulation  a  certain 
degree  of  concentration  of  the  calcium  ion  (or  barium  or 
strontium  ion)  is  necessary.  The  more  oxalate  present,  the 
lower  would  be  this  concentration,  so  that  a  certain  concen- 
tration of  the  free  oxalate  ion  (or  fluorine  ion)  is  necessary 
to  prevent  coagulation.  This  concentration  probably  de- 
pends in  part  upon  the  temperature. 

Another  coagulation  process  of  especial  interest  is  the 
precipitation  of  blood-plasma  by  means  of  fibrin-ferment 
(cf.  p.  91).  This  process  is  very  similar  to  the  coagula- 
tion of  milk  or  casein,  but  seems  to  be  different  in  the  fact 
that  coagulation  of  the  plasma  can  occur  spontaneously. 
According  to  Duclaux,  this  depends  upon  the  action  of 
the  leucocytes  present  in  the  blood.  In  their  cytolysis 
they  form  a  coagulating  ferment.  Coagulating  ferments 
that  act  upon  blood-plasma  are  very  common  in  the  differ- 
ent tissues,  fluids,  and  organs  of  the  body.  Alexander 


2/0  LECTURES  ON   IMMUNITY 

Schmidt  prepared  this  fibrin-ferment  by  precipitating  blood- 
serum  with  15  to  20  times  its  volume  of  alcohol.  The 
precipitate  was  filtered  and  dried.  This  precipitate  con- 
tains a  rather  large  quantity  of  fibrin-ferment  which  coagu- 
lates the  fibrin  contained  in  blood-plasma. 

It  is  possible  to  prepare  solutions  of  plasma  as  well  as 
of  fibrin-ferment  nearly  free  of  calcium  ions,  by  the  addi- 
tion of  oxalates  or  fluorides  to  the  blood.  On  mixing 
these  two  coagulations  occur,  although  there  are  oxalate 
ions  present  in  excess.  From  this  experiment  it  has  been 
concluded  that  calcium  ions  are  not  necessary  in  the  coagu- 
lation of  fibrin.  The  conclusion  is  not  quite  binding,  for 
there  are  always  calcium  ^ions  present,  although  in  very 
minute  quantity.  A  more  accurate  examination  of  this 
question  would  be  profitable.  On  the  other  hand,  it  is  cer- 
tain that  the  ions  of  calcium,  strontium,  and  barium  accel- 
erate to  a  high  degree  the  coagulation  of  fibrin.  On  the 
whole,  the  different  salts  seem  to  exert  upon  the  coagula- 
tion of  fibrin  an  influence  similar  to  that  upon  milk. 
The  presence  of  acids  is  favourable  to  the  plasmatic  coagu- 
lation. 

In  the  coagulation  of  plasma  (as  in  that  of  casein,  ac- 
cording to  Hammarsten's  investigations)  two  different 
phases  may  be  observed,  according  to  the  opinion  of  Bor- 
det  and  Gengou.1  The  one,  the  transformation  of  the  so- 
called  fibrinogen,  contained  in  the  plasma,  into  fibrin,  may 
proceed  as  the  result  of  the  action  of  the  ferment  in  the 
absence  of  calcium  salts ;  the  second  process,  the  coagula- 
tion, requires  the  presence  of  calcium  ions.  Hence  a 
perfect  analogy  exists  between  the  coagulations  of  plasma 
1Bordet  and  Gengou:  Ann,  de  Plnst.  Pasttur,  18.  26  (1904). 


THE  PRECIPITINS  AND  THEIR  ANTIBODIES 

and  of  casein.  This  duality  of  the  processes  recalls  the 
action  of  the  compound  haemolysins  in  which  at  first  the 
immune-body  is  absorbed  in  the  erythrocytes,  following 
which  the  formation  of  haemolysin  occurs.  According  to 
Bordet's  view,  the  parallelism  between  haemolysis  and  co- 
agulation is  still  more  prominent. 

Bordet  and  Gengou 1  suggest  that  the  action  of  fluorides 
on  blood-plasma  interferes  not  only  with  the  action  of  the 
Ca  ions,  which  are  precipitated  from  the  solution  as  CaFl2, 
but  also  with  that  of  the  fibrin-ferment,  which  is  carried 
down  from  the  solution  by  the  precipitate.  The  addition 
of  an  oxalate  does  not  interfere  sensibly  with  the  action 
of  the  ferment. 

Leo  Loeb2  found  a  certain  specificity  between  fibrin- 
ferment  and  plasma,  "  in  so  far  as  the  blood  of  each  species 
of  animal  used  coagulated  more  rapidly  under  the  influence 
of  the  tissues  of  animals  of  the  same  species  or  of  the 
tissues  of  related  animals  than  under  the  influence  of  the 
tissues  of  more  distant  animals."  The  addition  of  serum  of 
the  animal  producing  the  fibrin-ferment  increases  the  ac- 
tion. Even  the  products  of  bacteria  (especially  Strepto- 
coccus pyogenes  aureus)  are  sometimes  favourable  to  the 
coagulation. 

There  is  a  third  type  of  coagulation  provoked  by  a 
ferment.  In  certain  fruits  and  even  roots  of  plants  occurs 
a  substance  called  pectin.  This  substance  gives  with 
water  solutions  of  high  viscosity;  it  is  precipitated  by 
alcohol.  It  may  be  coagulated  by  means  of  a  ferment  called 

1  Bordet  and  Gengou:  Ann.  de  VInst.  Pasteur,  18.  98  (1904). 

2  Leo  Loeb:  Hofmeisters  Beitrage,  5.  534  (1904)  ;  Journ.  of  Medical  Re- 
search, 10.  407  (1903). 


2/2  LECTURES  ON  IMMUNITY 

pectase,  found  in  the  juice  of  carrots,  beets,  etc.  The  co- 
agulation is  hindered  by  the  presence  of  oxalate  ions,  i.e. 
the  presence  of  calcium  ions  (or  ions  of  barium  or  stron- 
tium) seems  necessary  also  in  this  reaction.  Acids  retard 
the  coagulation,  and  strong  mineral  acids  exert  a  greater 
influence  than  weak  vegetable  acids. 

Coagulation  or  precipitation  plays  a  very  important 
r61e  in  the  chemistry  of  antibodies.  We  have  already 
spoken  of  the  action  of  agglutinin  as  probably  associated 
with  a  coagulating  influence  upon  the  cells  (cf.  p.  164). 
The  agglutinating  power  of  acids  for  erythrocytes  is  fol- 
lowed by  a  very  obvious  coagulation.  Corrosive  sublimate 
produces  on  erythrocytes^both  coagulative  and  an  agglu- 
tinating action  in  higher  concentrations,  and  a  haemolytic 
action  in  lower  concentrations.  Haemolysis  and  coagula- 
tion (which  makes  itself  manifest  as  agglutination)  seem 
to  be  so  often  concomitant  in  the  so-called  phytalbumoses 
—  toxins  of  vegetable  origin,  as,  e.g.,  ricin  or  crotin  —  that 
Ehrlich  has  assumed  that  they  are  in  this  case  inseparable.1 
But  for  the  bacteriolysins  this  is  not  the  case,  according  to 
Kraus  and  Ludwig.2 

If  toxins  and  antitoxins  are  mixed  in  higher  concentra- 
tions, they  often  yield  a  precipitate.  Thus,  for  instance, 
Jacoby3  observed  a  flocculent  precipitate  on  mixing  ricin 
and  antiricin;  and  Hausmann4  made  a  similar  observation 
for  abrin  and  antiabrin.  Bashf ord  6  found  that  blood-serum 

1  Ehrlich  :  "  Schlussbetrachtungen  "  in  "  NothnagePs  spezielle  Pathologic 
und  Therapie,"  Bd.  8,  p.  13,  Vienna,  1901. 

2 Kraus  and  Ludwig:    Witn.  klin.  Wochenschrift,  No.  5  (1902). 
8 Jacoby:  Hofmeisters  Beitrage,  1.  51  (1901). 
4  Hausmann  :  Hofmeisters  Beitr'dge,  2.  134  (1902). 
6Bashford  :  Journ.  of  Pathology,  etc.,  8.  59  (1902). 


THE  PRECIPITINS  AND  THEIR  ANTIBODIES  2/3 

from  a  rabbit,  which  had  been  actively  immunised  against 
crotin,  gave  a  very  dense  precipitate  with  this  substance, 
a  precipitate  not  produced  with  normal  serum.  Myers 
showed  that  various  albuminous  bodies  (Witte  pepton,  crys- 
tallised egg-albumen,  serum  globulin)  injected  into  rabbits 
produced  precipitins  in  their  serum  which  acted  upon  the 
corresponding  albuminous  bodies  in  experiments  in  vitro}- 

"If  this  reaction  in  vitro"  Bashford  continues,  "be 
comparable  to  the  action  in  the  body,  then  the  injection 
of  a  solution  of  Witte  pepton  into  the  ear-vein  of  such  an 
immunised  animal  should  result  in  death  from  embolism." 
"  The  injection  very  slowly,  however,  of  5  c.c.  20  per 
cent  Witte  pepton  into  the  ear-vein  "of  a  highly  immu- 
nised rabbit  "  gave  no  symptoms."  "  The  reactions  in  vitro 
and  in  corpore  are  here  again  different.  Also  in  the  case 
of  a  rabbit  immunised  against  crotin ;  direct  injection  of 
my  albumin-containing  crotin-solution  had  no  consequence 
which  I  could  observe."  As  we  have  seen  before  (p.  205), 
the  equation  of  equilibrium  for  ricin  and  antiricin  is  not  of 
the  same  form,  if  we  investigate  the  action  of  this  poison 
on  red  blood-corpuscles  in  vitro  and  in  living  animals. 
From  this  circumstance  we  must  conclude  that  there  are 
different  poisons  acting  in  the  two  cases.  Ehrlich2  and 
Robert 3  supposed  that  the  two  poisons  were  identical,  and 
used  this  hypothesis  as  a  basis  for  theoretical  deductions. 
But  now  it  is  well  known  that  this  hypothesis  is  wrong. 

Even  for  tetanolysin  and  corrosive  sublimate  Bashford 
found  a  different  action  in  vitro  and  in  vivo.  Haemolysins, 

1  Myers  :   Centralbl.f.  Bakteriologie,  28  (1900). 
2 Ehrlich:  Fortschritte  de  Medidn,  15.  41  (1897). 

3 Robert:    Arbeiten   des  pharmakologischen  Instituts  zu  Dorpat,  Tome  8 
(cited  from  Bashford). 
T 


2/4  LECTURES  ON  IMMUNITY 

as  cyclamin,  saponin,  digitalin,  solanin,  cobra-venom,  and 
haemolytic  sera,  produce,  when  injected  into  living  animals, 
haemolysis,  which  is  manifested  by  haemoglobinuria.  "  It 
must,  however,  be  stated  that  the  actions  of  the  haemo- 
lysins  in  corpore  are  in  no  case  limited  to  the  erythro- 
cytes."  At  all  events,  it  seems  prudent  not  to  assume  a 
priori  that  the  actions  of  poisons  in  vitro  and  in  vivo  are 
identical. 

The  best  known  of  all  the  coagulating  substances  is  ren- 
net (or  chymosin).  It  seems  rather  probable  that  the  chief 
action  of  rennet  is  analogous  to  that  of  peptic  digestion, 
and  that  the  coagulation  is  a  mere  accidental  property 
belonging  to  the  products  of  the  digestion  at  higher  tem- 
perature (cf.  p.  267).  Be  that  as  it  may,  the  coagulation 
is  the  property  employed  hitherto  for  the  investigation  of 
the  action  of  rennet.  The  coagulating  power  of  rennet  is 
diminished  by  some  normal  sera,  especially  serum  from 
horses,  as  well  as  by  immune-sera  produced  by  the  injection 
of  rennet  into  animals,1  rabbits  being  especially  adapted  to 
this  purpose. 

Madsen  and  Walbum  have  investigated  the  neutralising 
power  of  this  "  antirennet "  and  found  that  it  behaves  just 
as  antitetanolysin  does  against  tetanolysin.  The  experi- 
mental method  was  the  following :  Mixtures  of  4  c.c.  of 
a  i  per  cent  solution  of  rennet  and  different  quantities 
(0.02-1  c.c.)  of  the  antirennet-containing  serum  and  of 
physiological  salt-solution  were  prepared  so  that  the  total 
quantity  was  5  c.c.  These  mixtures  were  held  at  room 

1Morgenroth:  {Centralbl.  f.  Bakteriologie,  i.  Abth.  26.  349,  1899,  and 
27.  721,  1900)  was  the  first  to  prepare  antirennet.  He  immunised  goats 
by  the  subcutaneous  injection  of  rennet.  After  repeated  injections  the  serum 
of  the  goat  contained  antirennet. 


THE  PRECttTTlNS  AND  THEIR  ANTIBODIES 


27§ 


temperature  (in  mean  16°  C.)  during  twenty  to  fifty  min- 
utes. Special  experiments  seemed  to  indicate  that  this  time 
of  reaction  has  no  notable  influence  if  it  only  exceeds  five 
minutes,  and  after  this  time  different  quantities  of  the  mix- 
ture were  added  to  10  c.c.  of  milk  and  physiological  salt- 
solution  added  up  to  12  c.c.  The  test-tubes  containing 
these  mixtures  were  placed  in  a  water-bath  of  constant 
temperature  and  the  coagulation  examined  after  a  given 
time  (two  hours).  The  calculation  for  the  experiment  is 
the  same  as  for  tetanolysin.  One  c.c.  of  the  antirennet 
was  found  equivalent  to  1.48  times  the  fixed  quantity  of 
rennet.  The  constant  of  equilibrium  was  found  to  be 
K  =  0.0 1 2.  n  is  the  quantity  of  antirennet  used. 

NEUTRALISATION  OF  RENNET  BY  MEANS  OF  IMMUNE-SERUM  FROM  RABBIT 


n  = 

***. 

^calc. 

A 

« 

**•, 

^calc. 

A 

0 

100 

100 

0.4 

42.6 

41.8 

±1-3 

0.02 

974 

97.1 

±  0.6 

0-5 

30.2 

28.2 

±  1.2 

0.05 

92.3 

92.6 

±1.4 

0.6 

16.5 

I6.5 

±0.4 

O.I 

85.9 

85.2 

±i-5 

0.7 

8.2 

8.4 

±0.6 

O.2 

70.4 

7O.6 

±1.8 

0.8 

4.7 

4-7 

±0.3 

0-3 

54-3 

56.0 

±1.9 

0.9 

2.8 

3-i 

±0.2 

The  experiments  are  rather  difficult  and  therefore  a  great 
number  of  observations  have  been  taken.  The  observed 
values  of  the  strength  of  the  rennet  in  the  mixture  are 
mean  values  of  not  less  than  eleven  different  measure- 
ments. Thanks  to  this  circumstance,  it  has  been  possible 
to  calculate  the  probable  error  of  each  value.  This  proba- 
ble error  is  tabulated  under  A.  As  is  seen  from  the 
comparison  of  ^calc.  with  g0^  the  difference  between  the 
calculated  values  and  the  observed  ones  are  in  eight  cases 


276  LECTURES   ON  IMMUNITY 

less  than  the  probable  error ;  only  in  two  do  they  exceed 
these,  and  even  then  not  greatly.  The  agreement  may  be 
regarded  as  striking,  and  the  whole  series,  which  is  the 
condensed  result  of  about  seven  hundred  and  fifty  tests,  — 
of  every  mixture  there  were  taken  six  to  eight  different 
tests  in  as  many  test-tubes,  —  may  be  regarded  as  a  model 
for  further  investigation  on  these  difficult  subjects. 

The  concordance  of  ^-calc.  with  gobtm  may  serve  as  a  very 
strong  proof  that  the  equation  used  for  the  calculation  is 
the  correct  expression  of  the  phenomenon. 

As  has  already  been  noted  (cf.  p.  3),  Hammarsten  and 
Roden 1  observed  that  normal  horse-serum  contains  a  sub- 
stance which  is  in  many  respects  similar  to  antirennet. 
Therefore  Madsen  and  Walbum  have  examined  this  anti- 
body in  a  similar  manner,  only  the  time  of  reaction  between 
the  two  antibodies  was  longer,  two  to  four  hours.  The 
results  of  experiments  with  two  different  preparations  are 
abridged  in  the  table  on  opposite  page. 

This  process  of  neutralisation  is  not  reproduced  by  the 
formula  valid  for  the  action  of  rennet  upon  antirennet, 
but  the  equation  is  the  same  as  that  valid  for  the  neutral- 
isation of  tetanolysin  by  means  of  cholesterin,  which 
indicates  that  one  molecule  of  rennet  and  one  of  the 
antibody  give  only  one  molecule  of  the  reaction-product. 
The  constants  are,  if  we  use  as  unit  concentration  that 
of  the  unneutralised  rennet  in  the  first  experiment,  for  the 
first  preparation  K  —  0.354,  and  for  the  second  K  —  0.138 ; 

1  Roden:  Upsala  lakareforenings  forhandlingar,  22.  546  (1887).  Roden 
observed  that  serum  of  swine  blood  is  nearly  as  active  as  that  of  horse  blood; 
sera  from  cattle  or  rabbits  have  a  much  weaker  action.  Even  ascites-fluid 
has  some  action.  The  active  substance  is  destroyed  by  heating  for  some  few 
minutes  to  70°  C.  or  even  by  treatment  with  alcohol. 


THE  PRECIPITINS  AND  THEIR  ANTIBODIES 

I  c.c.  of  the  first  serum  was  equivalent  to  2  times  the  fixed 
part  of  rennet  and  i  c.c.  of  the  second  serum  corresponded 
to  2.1  part  of  the  rennet.  The  observed  values  in  the 
first  series  are  mean  values  of  three,  and  in  the  second  of 
two  different  series  of  measurements. 

NEUTRALISATION  OF  RENNET  BY  MEANS  OF  NORMAL  HORSE-SERUM 


n 

*ob, 

^calc. 

• 

*obs. 

^calc. 

0 

100 

100 

O 

100 

100 

O.I 

80.0 

80.2 

0.02 

93-o 

96.3 

0.2 

64-3 

62.1 

0.05 

87.3 

90.9 

0.4 

51-7 

52.1 

O.I 

71.0 

82.0 

0.8 

33.5 

28.4 

0.2 

63.5 

65-3 

1.0 

24.9 

22.2 

0-3 

54-5 

49-5 

1.2 

21.0 

18.1 

0.4 

34-7 

38.3 

'•35 

1  6.0 

15.8 

0-5 

29.4 

28.9 

J-5 

13.5 

14.0 

0.6 

22.0 

22.2 

i-7 

10.0 

12.2 

0.8 

19.2 

144 

I.O 

9.4 

10.3 

1-3 

8.7 

7.1 

'•7 

3.1 

5-0 

2.0 

2.9 

4.0 

The  circumstance  that  the  neutralisation  of  the  antibody 
rom  normal  serum  follows  quite  different  laws  than  those 
alid  for  the  antirennet  produced  by  immunisation,  is  a 
ertain  indication  that  these  two  antibodies  are  really 
ifferent  substances.  This  is  also  probable  because  the 
ntirennet  is  much  more  easily  destroyed  by  heat  than  the 
ntibody  from  normal  serum.*  The  occurrence  of  many 
ntibodies  in  normal  sera  led  Ehrlich  to  the  supposition 

'This  criterion  gives  alone  no  absolutely  certain  indication, for  the  thermo- 
ihty  of  a   dissolved  substance  may  depend  to  a  rather  high  degree  on 
e  presence   of  other  substances,  as  salts  or  proteids  (^.  pepton),  in  the 
>lution.     Cf.  Biernacki:  Zeitschr.f.  Biologic,  28  (1891) 


278  LECTURES  ON  IMMUNITY 

that  animals  generally  produce  antibodies  against  different 
toxins  and  that  this  production  is  only  augmented  by  the 
experimental  injection  of  toxins  into  the  blood  of  the  ani- 
mal. In  other  words,  the  antibodies  in  normal  sera  ought 
to  be  identical  with  those  produced  after  active  immunisa- 
tion. This  is  evidently  not  true  for  the  antirennets.  There 
are  also  many  other  considerations  which  speak  against 
Ehrlich's  idea,  of  which  Bashford  has  given  a  detailed 
criticism.1 

In  one  point  I  cannot  agree  with  Bashford.  He  assumes 
that  the  toxin,  i.e.  in  this  case  the  rennet,  is  divided  between 
the  normal  serum  and  the  rest  of  the  fluid.  This  is  quite 
like  the  idea  held  by  Biltz.  According  to  Bashford,  if  for 
the  second  serum  0.3  c.c.  of  the  serum  takes  half  of  the 
rennet,  then  0.6  c.c.  ought  to  fix  two-thirds  of  it,  whereas 
it  actually  takes  78  per  cent;  0.9  c.c.  should  fix  75  per  cent, 
whereas  the  table  gives  88;  1.2  c.c.  should  carry  80  per 
cent,  instead  of  the  91  per  cent  observed. 

This  last  series  may  be  calculated  according  to  the 
scheme  of  Biltz;  it  gives  a  nearly  constant  value  of  the 
exponent  /,  viz.  /  =  2.3  (cf.  p.  216).  But  the  first  series 
for  normal  horse-serum  yields  a  steadily  increasing  value 
of/  with  increasing  n.  Between  n  =  o.i  and  n  —  0.4,  /  is 
0.85 ;  between  n  —  0.4  and  n  —  i.o,  we  find  /  =  1.5  ;  be- 
tween n  =  i.o  and  n  =  1.5,  /  is  2.4;  for  higher  values  of 
n,  p  is  found  to  be  3.3. 

If  we  apply  the  idea  of  Biltz  to  the  fixation  of  rennet 
to  antirennet,  we  find  that  at  first  the  concentration  oil 
rennet  in  the  serum  is  constant  until  about  n  —  0.6,  whereas 
that  of  the  rennet  in  the  fluid  sinks  in  the  proportion  6  to  i 

1  Bashford:  Journ.  of  Pathology,  8.  62  (1902). 


THE  PRECIPITINS  AND  THEIR  ANTIBODIES  279 

which  is  evidently  impossible,/  is  infinite.  Then/  passes 
through  the  value  12  between  n  =  0.6  to  0.7,  and  sinks 
to  5.3  between  n  —  0.8  and  n  —  0.9. 

In  a  very  excellent  memoir  Fuld  and  Spiro1  have  made 
it  probable  that  the  "  antirennet "  contained  in  the  normal 
serum  of  horse  blood  is  a  so-called  pseudo-globulin  2  which 
acts  in  such  a  manner  that  it  binds  a  part  of  the  calcium 
ions  and  thereby  hinders,  or  better  retards,  the  coagulation. 
As  we  have  seen  before  (cf.  p.  74),  the  influence  of  the 
quantity  of  free  calcium  ions  upon  the  time  of  coagulation 
is  as  large  as  that  of  the  quantity  of  rennet.  Therefore 
a  binding  of  the  calcium  ions  in  a  certain  proportion  has 
the  same  effect  as  a  neutralisation  of  rennet  in  the  same 
proportion.  In  this  case  the  quantity  of  calcium  salt  of 
the  para-casein  regulates  the  velocity  of  coagulation.  The 
salts  of  calcium  with  para-casein  and  with  the  pseudo- 
globulin  must  be  dissociated  to  a  very  low  degree,  and 
for  the  sake  of  simplicity  we  may  suppose  that  the  degree 
of  dissociation  of  the  two  salts  and  of  the  acids  in  the  pres- 
ence of  a  given  quantity  of  calcium  ions  is  such  that  we 
may  make  use  of  the  formula  of  Guldberg  and  Waage. 
This  may  at  least  be  regarded  as  a  preliminary  approxima- 
tion, which  we  may  employ  until  the  properties  of  the 
reacting  compounds  have  been  better  examined.  Then  if 
the  quantity  of  para-caseate  of  calcium  in  the  absence  of 

1  Fuld  and  Spiro:   Zeitschr.  f.  ph.  Ch.,  31.  147  (1900). 

2  On  precipitation  with  ammonium  sulphate,  euglobulin  and  pseudo-globu- 
lin separate  out.     Their  aqueous  solution  is   dialysed,  then  the  euglobulin 
precipitates  and  the  pseudo-globulin  remains  in  solution.    The  euglobulin  has 
a  coagulating  influence  on  casein.     The  pseudo-globulin  retards  the  coagu- 
lation, even  if  caused  by  papayotin,  cynarase  or  euglobulin,  as  well  as  by 
rennet. 


280 


LECTURES  ON  IMMUNITY 


serum  be  taken  as  a  unit,  this  may  be  regarded  as  nearly 
equivalent  to  the  quantity  of  calcium  present,. if  it  does  not 
exceed  a  certain  limit ;  now  n  equivalents  of  pseudo-globulin 
are  added,  then  at  equilibrium  we  have  (n  —  x)  equivalents 
of  pseudo-globulin,  (i  —  x)  equivalents  of  calcium  para- 
caseate,  x  equivalents  of  calcium  salt  of  the  pseudo-globu- 
lin, and  (a  +  x)  equivalents  of  para-casein,  where  a  is  the 
quantity  of  free  para-casein  for  n  =  o.  Then  the  equi- 
librium follows  the  equation 

(n-  x)(\-  x)  =  K-x(a+x). 

If  a  is  high,  i.e.  in  the  presence  of  much  casein,  we  may 
regard  (a  +  x)  as  a  constant,  and  we  have  the  equation  with 
the  aid  of  which  the  calculated  values  above  have  been 
derived.  We  may  therefore  say  that  the  opinion  of  Fuld 
and  Spiro  agrees  with  the  experiments,  and  it  is  easy  to  see 
how  these  might  be  controlled  to  a  still  higher  degree. 

Even  against  the  coagulation  of  blood-plasma  there  exist 
some  natural  antibodies,  one  of  which,  the  hirudin,  the 
extract  of  leeches,  has  been  known  for  a  long  time.  Fuld 
and  Spiro l  made  the  following  determinations  of  the  quan- 
tity of  "free  muscle  extract"  from  goose,  of  which  0.4  c.c. 
had  been  taken,  in  the  presence  of  n  c.c.  of  an  extract  of 
leeches,  acting  on  i  c.c.  of  goose  plasma. 
NEUTRALISATION  OF  MUSCLE  EXTRACT  FROM  GOOSE  BY  MEANS  OF  HIRUDIN 


n 

*<*•. 

^calc. 

0 

100 

100 

0.2 

75-0 

82.0 

0.4 

66.7 

64.9 

0.8 

357 

36.0 

1.6 

ii.  i 

II.  2 

1  Fuld  and  Spiro:  Hofmcisters  Beitrage^  5.  181  (1904). 


THE  PRECIPITINS  AND  THEIR  ANTIBODIES  281 

For  the  calculation  the  formula  used  was  that  employed 
before  for  the  calculation  of  the  influence  of  horse-serum 
on  rennet.  Of  the  solution  of  hirudin  i  c.c.  is  equivalent 
to  the  fixed  quantity  (0.4  c.c.)  of  the  extract,  and  the  con- 
stant is  K  =  0.09.  The  agreement  is  very  satisfying. 
It  therefore  seems  quite  proper  to  assume  that  the  action 
of  hirudin  on  the  coagulation  of  blood-plasma  is  of  the 
same  nature  as  the  action  of  pseudo-globulin  on  the  co- 
agulation of  casein. 

The  circumstance  that  the  substances  concerned  in  bio- 
chemistry react  not  only  with  their  specific  antibodies,  but 
also  with  other  compounds,  specially  with  such  well-known 
properties  as  acids,  bases,  salts,  or  even  lecithin  and 
cholesterin,  is  a  very  promising  feature.  For  if  there 
were  no  reactions  except  with  the  specific  antibodies,  which 
we  have  very  little  hope  of  obtaining  in  the  pure  state 
adapted  to  a  detailed  investigation,  we  would  have  very 
slight  prospects  of  rapid  progress. 

Besides  the  coagulating  ferments  there  is  another  group 
of  precipitins  which  deserve  this  name  to  a  higher  degree, 
namely,  those  prepared  by  injection  into  living  animals  of 
fluids  containing  proteins.  Among  these  the  lacto-serum, 
which  is  obtained  by  the  injection  of  milk  into  animals,  has 
been  investigated  very  thoroughly  by  P.  T.  Miiller.1  Other 
precipitins  produced  by  the  intraperitoneal  injection  of 
egg-albumen  or  normal  horse-serum  into  rabbits  were 
studied  by  Eisenberg;2  they  behaved  very  like  the  lacto- 
serum  prepared  by  the  intraperitoneal  injection  into  rabbits 
and  studied  by  Miiller. 

JP.  T.  Miiller:  Archiv  f.  Hygiene,  44.  126  (1902);  Centralbl  f.  Bah- 
teriologie,  etc.,  32.  521  (1902),  and  34.  48  (1903). 

2  Eisenberg:  Bull,  de  VAc.  des  Sciences  de  Cracovic,  p.  289  (1902). 


282  LECTURES  ON  IMMUNITY 

Bordet1  early  drew  attention  to  the  great  difference 
between  rennet  and  lacto-serum,  though  both  coagulate 
milk  (casein).  The  coagulation  with  rennet  is  much  more 
voluminous  and  gelatinous  than  that  with  lacto-serum, 
which  also  gives  precipitation  at  lower  temperatures 
(under  20°  C.),  very  different  from  rennet.  Furthermore, 
lacto-serum  is  inactivated  only  by  being  heated  for  thirty 
minutes  to  over  70°  C.,  whereas  a  2  per  cent  solution  of 
rennet  loses  its  coagulative  power  in  less  than  five  minutes 
at  50°  C.  (cf.  p.  87).  The  lacto-serum  is,  on  the  other 
hand,  much  more  easily  precipitated  by  ammonium  sul- 
phate than  is  rennet.  A  very  important  point  is  that  the 
coagulum  of  the  lacto-serum  yields  no  serum-albumen.  A 
similarity  is  that  in  both  cases  the  presence  of  calcium  or 
barium  salts  is  necessary  for  the  precipitation,  so  that  the 
reaction  is  hindered  by  the  presence  of  oxalates  in  the 
milk.  M tiller  investigated  other  salts,  viz.  NaCl,  KC1, 
NH4C1,  Na2HP04,  NaCH3CO2,  NaNO3,  KNO3,  KI, 
KBr,  KSCN,  and  MgSO4,  but  none  of  them  could  replace 
Ca  salts.  In  this  point  there  is  a  great  distinction  from 
the  agglutinations,  which  are  rendered  possible  by  the 
most  widely  different  salts  (cf.  p.  159)  according  to  Fried- 
berger.2  The  precipitins  examined  by  Eisenberg  do  not 
seem  to  need  salts  for  their  action.  Many  salts  diminish 
the  action  in  even  rather  weak  concentrations,  thus,  for 
instance,  (NH4)2SO4  in  0.25  normal  solution  and  MgCl2 
in  2  normal  solution  completely  check  the  precipitating 
action.  By  heating  the  milk  during  some  time  to  100°  C. 

1  Bordet:  Ann.  de  VInst.  Pasteur,  13.  241  (1899). 

2  Frierlberger :    Centralbl.  f.  Bakteriologie,  30.   341(1901).    Cf.  Bechhold; 
p.  159  above. 


THE  PRECIPITINS  AND  THEIR  ANTIBODIES  283 

or  egg-albumen  to  78°  C.  during  60-90  minutes,  their 
precipitability  was  lost.  But  M  tiller  found  that  the  pre- 
cipitation by  lacto-serum  could  be  restored  by  the  addition 
of  Ca  salts,  or  even  that  it  would  not  disappear  if  the 
milk  contained  naturally  much  calcium.  Concentrated 
solutions  of  urea  or  formalin  destroy  the  precipitability  of 
egg-albumen  as  well  as  the  agglutinability  of  bacteria. 

The  precipitate  from  a  mixture  of  milk  and  lacto-serum 
dissolves  in  a  i  per  cent  solution  of  NaCl.  This  solution 
can  be  precipitated  again  by  rennet  or  lacto-serum,  just 
as  a  solution  of  casein.  The  treatment  with  rennet  also 
yielded  serum-albumen.  Evidently  the  precipitate  is 
somewhat  soluble,  and  in  solution  partly  dissociated  into 
the  two  components.  At  high  temperature  the  free  lacto- 
serum  is  decomposed  and  new  quantities  of  lacto-serum  are 
successively  formed  by  the  decomposition  of  the  soluble 
fraction  of  the  precipitate  until  this  is  wholly  reconverted 
into  casein.  M  tiller  also  isolated  the  lacto-serum  from  the 
precipitate  through  cautious  treatment  with  acetic  acid; 
the  liquid  obtained  by  centrifugation  of  the  precipitate, 
which  had  been  in  contact  with  the  acid  solution  for  two 
hours,  contained  a  noticeable  quantity  of  precipitin.  The 
compound  of  lacto-serum  and  casein  may  be  precipitated 
by  the  sudden  addition  of  acetic  acid.  The  precipitate  dis- 
solves completely  upon  neutralisation,  but  is  precipitated 
by  small  quantities  of  a  calcium  salt.  The  compound, 
therefore,  probably  exists  in  the  solution,  but  in  a  partially 
dissociated  state,  and  gives  an  insoluble  product  with 
calcium  or  barium  salts.  Para-casein,  prepared  by  the 
action  of  rennet  on  milk,  does  not  bind  the  lacto-serum. 

The   lacto-serum   heated  to   70°  C.  for  thirty  minutes 


284  LECTURES  ON  IMMUNITY 

acquires  the  peculiar  property  of  hindering  the  precipita- 
tion of  casein  by  means  of  lacto-serum.  In  the  same 
manner  Eisenberg  found  that  his  precipitin  for  egg-albu- 
men on  heating  for  one  hour  to  72°  C.  was  transformed 
into  an  antiprecipitin.  In  the  same  manner  the  precipi- 
tins  against  cholera  and  typhoid,  prepared  by  injection  of 
cultures  of  the  corresponding  bacteria  into  the  veins  of  a 
horse,  lose  their  property  of  coagulating  the  correspond- 
ing bacterium  on  being  heated  for  thirty  minutes  to  about 
60°  C.,1  and  acquire  anticoagulating  properties  on  heating 
to  73°  C.  (for  cholera-serum).  Even  for  the  agglutinins, 
similar  observations  have  been  made  by  Eisenberg  and 
Volk.  Through  different  experiments  Miiller  was  led  to 
the  conclusion  that  the  antiprecipitin  binds  the  casein, 
with  which  it  gives  a  compound  soluble  in  the  presence  of 
calcium  salts.  Antiprecipitin  may  even  dissolve  the  pre- 
cipitate, in  the  same  manner  as  a  carbonate  is  dissolved  by 
a  not  too  weak  acid.  This  was  shown  in  a  simple  manner 
by  Eisenberg,  by  preparing  in  one  test  a  mixture  of  pre- 
cipitin and  antiprecipitin  with  egg-albumen,  and  in  a 
second  test  a  mixture  of  antiprecipitin  and  egg-albumen 
with  precipitin.  In  the  second  case  no  precipitate  was 
formed  because  the  egg-albumen  was  bound  by  the  anti- 
precipitin, while  in  the  first  case  precipitation  occurred. 
(The  velocity  of  reaction  is  evidently  rather  slow,  otherwise 
the  two  experiments  would  give  the  same  result.)  Similar 
experiments  were  made  by  Eisenberg  with  coagulating 
serum  antagonistic  to  the  bouillon  of  typhoid  cultures. 
The  antiprecipitins  are  derived  from  the  precipitins,  for 
after  these  have  been  precipitated  from  the  serum  (for 

1  Pick:  Hofmeisters  Beitragc,  1.  8 1  (1901). 


THE  PRECIPITINS  AND  THEIR  ANTIBODIES  285 

instance,  from  lacto-serum  by  means  of  milk),  it  yields  no 
antiprecipitin  on  being  heated ;  normal  serum  likewise 
gives  no  antiprecipitin. 

The  binding  of  precipitin  to  casein  may  be  judged,  on 
the  basis  of  the  insignificant  solubility  of  the  compound,  to 
be  nearly  complete  if  the  two  substances  are  present 
in  equivalent  quantities.  If  one  of  them  is  present  in  the 
fluid  in  excess,  it  is  to  a  large  extent  carried  down  by  the 
precipitate.  Especially  is  this  valid  for  precipitin.  With 
the  precipitable  substance  there  is  another  perturbing 
influence,  which  is  especially  prominent  with  egg-albumen 
and  which  has  its  analogies  in  the  behaviours  of  agglu- 
tinins  and  serum-precipitins.  An  excess  of  egg-albumen 
dissolves  the  precipitate,  so  that  it  is  often  observed  that 
a  given  quantity  of  precipitin  causes  a  precipitate  with  a 
weak  but  not  with  a  stronger  solution  of  egg-albumen. 
Even  with  casein  this  peculiarity  may  be  observed,  as 
Miiller's  later  experiments  indicate.  The  quantity  of  the 
precipitate  produced  by  a  given  quantity  of  lacto-serum 
therefore  increases  at  first  with  the  quantity  of  casein 
added,  and  reaches  a  maximum  in  the  neighbourhood  of  the 
point  where  the  casein  added  is  equivalent  to  the  quantity 
of  lacto-serum,  only  to  decrease  thereafter  and  fall  to  zero 
at  a  point  where  the  quantity  of  casein  added  is  nearly 
double  that  corresponding  to  the  maximum  value;  the 
determinations  do  not  seem  to  be  accurate  enough  to 
warrant  more  than  an  approximative  valuation. 

Some  experiments  of  Eisenberg  afford  an  idea  of  the 
relations  between  antiprecipitin  and  precipitin.  The  quan- 
tities of  the  preparations  are  given  in  drops.  The  antiserum 
was  heated  precipitin  diluted  in  the  proportion  I  to  5. 


286 


LECTURES  ON  IMMUNITY 


A  is  the  quantity  of  egg-albumen,  B  the  quantity  of  pre- 
cipitin,  C  that  of  antiprecipitin,  D  the  rest  of  the  fluid 
given  in  quantity  of  physiological  salt-solution.  The  total 
quantity  was  always  about  sixty  drops. 

ANTAGONISM  BETWEEN  PRECIPITIN  AND  ANTIPRECIPITIN 


A 

B 

C 

D 

OBS. 

P 

0.6 

0 

58 

Free. 

0.6 

1.2 

i 

56 

No 

0.38 

3 

i 

55 

Free. 

0.6 

12 

5 

42 

No 

o-55 

30 

5 

24 

Trace 

0.75 

53 

5 

i 

Free. 

0.84 

44 

15 

o 

No 

0-59 

3 

3 

15 

39 

No 

0.27 

10 

3 

15 

32 

Free. 

0.9 

The  results  may  be  calculated  on  the  supposition  that 
the  antiprecipitin  is  double  as  strong  as  the  precipitin,  i.e. 
one  drop  of  the  antiprecipitin  contains  double  the  number 
of  equivalents  as  one  drop  of  precipitin,  and  that  the  egg- 
albumen  is  divided  equally  between  the  different  equiva- 
lents. Then  the  precipitate  P  formed  may  be  calculated 
from  the  formula  :  — 


P  = 


2C 


-A. 


I  have  therefore  calculated  this  expression  and  tabulated  it 
under  P.  It  will  be  seen  that  if  P  equals  0.6  or  is  greater, 
precipitation  is  observed  ;  if  it  is  less,  not. 

The  precipitate  from  egg-albumen  is  soluble  in  weak 
solutions  of  acids  or  bases,  but  insoluble  even  in  concen- 
trated solution  of  sodium  chloride.  The  acid  solution 
yields  precipitation  on  neutralisation.  On  heating,  it  coag- 


THE   PRECIPITINS  AND  THEIR  ANTIBODIES  287 

ulates,  so  that  it  loses  its  solubility  in  weak  acids.  In 
this  point  it  differs  from  the  lacto-serum  precipitate  and 
from  agglutinated  bacteria,  which  lose  their  agglutination 
at  high  temperatures.  It  is  soluble  in  concentrated  solu- 
tions of  urea  or  magnesium  chloride  or  in  formalin.  In 
this  point  it  resembles  agglutinated  bacteria. 

A  great  practical  importance  is  attached  to  the  examina- 
tion of  the  properties  of  serum-precipitins,  prepared  by 
the  injection  of  serum  from  one  animal  into  the  veins  of 
another  animal.  These  precipitins  are  to  a  high  degree 
specific,  and  they  have  therefore  been  used  to  determine  the 
origin  of  blood-flecks  for  forensic  or  medico-legal  purposes. 
On  this  point  it  may  be  sufficient  here  to  refer  to  the 
investigations  of  Uhlenhuth,1  Wassermann  and  Schutze,2 
and  Hamburger.3 

Recently  Hamburger4  has  executed  some  quantitative 
experiments  on  the  action  of  these  precipitins.  He  meas- 
ured the  precipitate  formed  in  the  reaction  between  a 
certain  quantity  of  a  blood-serum  and  its  antibody  pro- 
duced by  the  repeated  injections  of  this  serum  into  the 
veins  of  another  animal.  The  reacting  fluids  were  mixed 
in  a  funnel-shaped  vessel  which  extended  into  a  capillary 
tube  of  uniform  calibre  and  graduated  in  100  divisions. 
By  vigorous  centrifugation  of  this  vessel  for  1.5  to  2  hours 
he  packed  the  precipitate  into  the  capillary  tube,  where  it 
reached  a  constant  volume  and  was  measured  by  the  read- 
ing of  the  divisions. 


1  Uhlenhuth:  Deutsche  med.  Wochenschrift,  No.  30,  p.  499  (1901). 

2  Wassermann  and  Schutze :  Berl.  klin.  Wochenschrift  (1901). 
8  Hamburger:  Deutsche  med.  Wochenschrift,  No.  6  (1905). 

*  Hamburger:  Folia  hcematologica,  Vol.  2,  No.  8  (1905). 


288  LECTURES  ON  IMMUNITY 

One  series  of  experiments  was  done  with  serum  (A) 
from  horse  blood  and  serum  (B)  from  a  calf  which 
had  been  treated  with  horse-serum  several  times.  The 
horse-serum  was  diluted  with  50  times  its  volume  of  a 
i  per  cent  solution  of  sodium  chloride.  If  to  a  certain 
quantity,  i  c.c.,  of  the  calf-serum  increasing  quantities  of 
horse-serum  (A)  were  added,  at  first  no  precipitate  ap- 
peared; then  at  higher  concentrations  of  A  the  quantity 
of  precipitate  increased  nearly  proportionally  to  the  quan- 
tity of  A  added  until  a  maximum  was  reached.  Thereafter 
further  additions  of  horse-serum  caused  the  quantity  of 
precipitate  to  decrease  until  -at  a  certain  limit  the  precipi- 
tate again  disappeared.  This  behaviour,  which  is  very 
common  in  reactions  between  sera  and  their  precipitins, 
is  clearly  apparent  from  the  following  figures.1  In  this 
case  the  total  volume  (100  div.)  of  the  capillary  tube 
was  0.04  c.c.  The  precipitate  is  therefore  in  the  fol- 
lowing table  given  in  units  of  0.0x304  c.c.,  corresponding 
to  one  division.  One  c.c.  of  calf-serum  is  fixed  as  100 
units,  corresponding  to  the  fact  deduced  from  the  experi- 
ments that  it  could  yield  in  maximo  100  units  of  precipi- 
tate, P\  and  i  c.c.  of  the  diluted  horse-serum  is  on 
analogous  grounds  fixed  as  300,  so  that  i  c.c.  of  A  is 
equivalent  to  3  c.c.  of  B.  This  seems  to  indicate  that 
nearly  the  whole  quantity  of  the  albuminous  substances 
in  A,  but  only  a  very  small  fraction  of  those  in  B,  enter 
into  the  precipitate. 

The  maximum  is  reached  at  A  =  100;  that  is,  on  the 
addition  of  0.333  c«c-  of  horse-serum,  the  quantity  equiva- 

1  Hamburger  and  Arrhenius:  Proc.  of  the  Meeting  of  the  R.  Ac.  of 
Sciences,  in  Amsterdam,  May  26,  1906,  p.  33. 


THE  PRECIPITINS  AND  THEIR  ANTIBODIES 


289 


lent  to  the  quantity  of  calf-serum  present.  (This  observa- 
tion has  really  led  to  the  determination  of  the  equivalent 
quantities  of  the  two  sera.) 

ACTION  OF  DIFFERENT  QUANTITIES  {A}  OF  HORSE-SERUM  ON  A  GIVEN 
QUANTITY  (100)  OF  CALF-SERUM 


A 

VOL. 

•^obs. 

Pc&lc. 

A 

VOL. 

•^obs. 

-^calc. 

4 

I.OI3 

0 

O.2 

79 

.267 

51 

53-6 

8 

1.027 

3 

3-9 

88.3 

.294 

55 

57-1 

'5 

•°5 

10 

10.3 

90 

•3 

57 

57-5 

24 

.08 

17 

17.8 

100 

•333 

59 

58.9 

30 

,i 

21 

23.6 

"54 

•385 

55 

57-4 

39 

•13 

32 

29.7 

137 

•457 

5° 

5L3 

45 

•15 

34 

34-0 

167 

•557 

43 

4i.3 

54 

.18 

43 

40.1 

214 

.713 

25 

26.8 

60 

.2 

45 

43-9 

300 

2.0 

5 

5-5 

75 

1.25 

(53 
(5i 

5i-9 

500 

2.67 

2 

o 

The  calculated  figures,  which  within  the  errors  of  ob- 
servation agree  with  the  observed  values  —  the  magnitude 
of  the  errors  of  observation  may  be  judged  by  the  differ- 
ence of  the  two  observations  for  ^4  =  75  —  are  found  in 
the  following  manner :  The  quantity  B  of  calf-serum  (in 
this  case  B  =  100)  may  react  with  A  equivalents  of  horse- 
serum.  Then  a  certain  amount  of  precipitate,  Plt  is 
formed,  of  which  /  parts  are  soluble  in  i  c.c.  and  the 
rest,  P1  —p  V=  P,  is  packed  in  the  capillary  tube  (y  is 
the  volume  of  the  mixture).  Then  there  are  remaining  in 
the  solution  A  —  Pl  equivalents  of  horse-serum,  and  B  —  Pl 
equivalents  of  calf-serum.  But  experience  indicates  that 
a  further  addition  of  horse-serum  dissolves  the  precipitate. 
Let  us  suppose  that  there  are  formed  Y  equivalents  of 


290  LECTURES  ON   IMMUNITY 

soluble  compound,  such  that  one  equivalent  of  it  contains 
one  equivalent  of  precipitate  and  n  equivalents  of  horse- 
serum  (or  in  other  words  n  +  I  equivalents  of  horse-serum 
and  i  equivalent  of  calf-serum).  Then  there  are  present 
in  the  solution  the  following  quantities  in  equivalents  of 
the  different  substances  :  — 

(A  -  P  —p  V—  (n  +  i)  F)  of  horse-serum, 
(B-P-p  V-  Y)  of  calf-serum  ; 

and  the  following  equations  of  equilibrium  are  valid  :  — 
\A-P-pV-(n+i)Y\  {B-P-pV-Yl^ 


If  we  determine  Ffrom  the  last  equation  and  introduce 
it  into  the  first  one,  we  obtain  :  — 


/  is  found  in  the  experiments  to  be  2.5.  If  we  put 
^  +  «  +  i  =  345  and  ATi/""  -  ^±i£±0/  =  T  30,  we  find 

/  A2 

the  calculated  values  of  the  total  quantity  (P)  of  precipi- 
tate. The  tabulated  values  of  P  give  this  quantity  divided 
with  the  volume,  Vt  i.e.  the  quantity  of  precipitate  in  i  c.c. 

J£     jjm,  +  1 

The  last  equation  gives  -~  —  --  =130.     If  we  suppose 

A2    0.29 

m  =  i,  i.e.  that  one  molecule  of  precipitate  is  formed  from 
one  molecule  of  each  of  its  two  components,  we  obtain 

K+  .  K,      3.08 

—  i  =  3.08  ;  if  we  suppose  m  =  2,we  find  —  ^  =  —  —  =  0.879. 

A2  A2        / 


THE   PRECIPITINS  AND  THEIR  ANTIBODIES  29 1 

These  two  assumptions  regarding  m  seem  the  most  prob- 
able. In  the  first  case  the  constants  of  reaction  are  of  the 
same  order  of  magnitude;  in  the  second  case  K^  is  of  the 
same  order  of  magnitude  as  K^p.  As,  further,  n  =  2.45  — 

TS-  -IS" 

— -,  and  — -  has  a  positive  value,  n  can  only  be  I  or  2  (if  we  do 

not  take  into  consideration  fraction  numbers).  The  proba- 
bility is  therefore  that  the  soluble  compound  of  precipitate 
with  the  active  fraction  of  the  horse-serum  is  built  up  of  one 
molecule  of  the  precipitate  and  one  or  two  molecules  of 
the  other  reacting  substance. 

In  some  cases  it  is  not  necessary  to  assume  that  the 
precipitate  is  dissolved  on  the  further  addition  of  the 
serum  which  has  been  injected.  A  very  interesting 
instance  of  this  behaviour  is  given  by  Hamburger  in 
the  action  of  the  serum  of  a  rabbit  treated  with  sheep- 
serum  on  the  sera  of  three  different  animals,  viz. :  sheep, 
goat,  and  bullock,  which  are  so  closely  related  to  each 
other  that  all  yield  precipitates  with  the  said  rabbit-serum. 
As  is  natural,  the  sheep-serum  yielded  the  most  voluminous 
precipitate ;  next  comes  the  goat-serum,  which  animal  is 
the  most  closely  related  to  the  sheep ;  and  the  least  quan- 
tity of  precipitate  is  given  by  the  serum  from  the  bullock, 
which  is  less  closely  related  to  the  sheep  than  is  the  goat. 
The  figures  are  given  in  the  following  three  tables.  The 
rabbit-serum  was  always  used  in  the  quantity  of  0.4  c.c. 

The  quantity  of  the  precipitate  is  given  in  scale-divisions 
of  the  capillary  tube  (100  divisions  =  0.04  c.c.).  The  sheep- 
serum  was  normal  serum  diluted  with  49  times  its  volume 
of  i  per  cent  solution  of  sodium  chloride.  The  sera  of 
goat  and  bullock  used  in  the  following  two  series  of  ex- 


292 


LECTURES  ON   IMMUNITY 


ACTION  OF  SERUM  FROM  A  RABBIT,  IMMUNISED  WITH  SHEEP-SERUM,  ON 
SHEEP-SERUM    ^ 


QUANTITY  OF  A 

r. 

QUANTITY  P  OF  PRECIPITATE 

c.c. 

Equiv. 

obs. 

calc. 

0.02 

0.8 

0.162 

I 

0-5 

0.04 

1.6 

0.163 

2 

!-3 

O.I 

4 

0.25 

3 

3.5 

O.I5 

6 

0.302 

6 

5-3 

0.2 

8 

0.36 

7 

7.2 

0.6 

24 

1.  00 

21 

21.5 

I 

40 

1.96 

35 

34 

1.5 

60 

3.61 

39 

48 

2 

80 

'   5.76 

60 

57 

3 

120 

11.56 

67 

66 

5 

200 

29.2 

64 

65 

7 

280 

54-8 

58 

58 

IO 

400 

108.2 

49 

46 

15 

600 

237 

10 

19 

18 

720 

338 

5 

3 

20 

800 

416 

2 

o 

i  (  +  i  c.c.  aq.) 

40 

5.76 

28 

25 

5  (  +  i  c.c.  aq.) 

200 

41 

57 

51 

IO  (  -f  I  c.c.  aq.) 

4OO 

130 

41 

32 

periments  were  also  diluted  in  the  same  manner.  The 
experiments  were  calculated  in  the  following  manner,  i 
c.c.  of  the  sheep-serum  is  equivalent  to  40  units  of  precipi- 
tate. The  number  of  such  equivalents  of  sheep-serum  is 
given  in  the  second  column.  In  the  same  manner  0.4  c.c. 
of  rabbit-serum  contains  120  such  equivalents,  i.e.  i  c.c. 
contains  300  equivalents.  If  now  the  volume  is  V,  con- 
taining originally  A  equivalents  of  sheep-serum  and  120 
equivalents  of  rabbit-serum,  and  P  equivalents  of  precipi- 
tate have  been  formed,  then  the  concentrations  of  the  two 


THE  PRECIPITINS  AND  THEIR  ANTIBODIES  293 

(A-P)          ,    (I20-P) 

sera  are  a  —  ^  —  /  and  -    —  —  —  %  and  the  formula  repre- 
senting the  equilibrium  is:  — 


where  K  is  a  constant,  which  according  to  the  experiments 
is  250.  With  the  aid  of  this  equation  the  calculated  values 
of  P  have  been  found  and  are  written  beside  the  observed 
values.  In  the  three  last  tests  i  c.c.  of  water  containing 
I  per  cent  of  sodium  chloride  has  been  added  to  the  mix- 
ture of  the  sera,  which  circumstance  has  been  taken  ac- 
count of  in  the  calculation  of  the  volume  F(in  c.c.). 

The  agreement  between  the  observed  and  the  calculated 
values  may  be  regarded  as  very  satisfying,  especially  with 
respect  to  the  enormous  change  of  A  (in  the  proportion  of 
i  :  1000)  and  of  F2  (i  :  2500). 

The  simple  form  of  the  equation  of  equilibrium  depends 
upon  two  circumstances  :  the  extremely  low  solubility  of  the 
precipitate  in  rabbit-serum  (not  i  in  3000),  and  in  sheep- 
serum.  Probably  these  two  circumstances  are  connected 
with  each  other.  The  figures  obtained  with  goat-serum 
were  calculated  in  the  same  manner  and  the  results  are 
given  below.  In  this  case  I  c.c.  of  the  goat-serum  was 
always  equivalent  to  40  units  of  the  precipitate,  but  0.4  c.c. 
of  the  rabbit-  serum  was  equivalent  to  only  85  units  of  pre- 
cipitate. 

The  constant  K  is  set  at  200.  Here  the  agreement  is 
not  so  perfect  as  in  the  foregoing  series.  The  agreement 
would  have  been  much  closer  for  the  latter  part  of  this 
series  if  we  had  taken  K  =  160,  but  then  the  first  part 
would  have  shown  greater  deviations  than  it  does  now; 


294 


LECTURES   ON   IMMUNITY 


ACTION  OF  SERUM  FROM  A  RABBIT,  IMMUNISED  WITH  SHEEP-SERUM,  ON 
GOAT-SERUM  (A) 


QUANTITY  OF  A 

V* 

QUANTITY  P  OF  PRECIPITATE 

c.c. 

Equiv. 

obs. 

calc. 

0.02 

0.8 

0.162 

I 

0.4 

0.04 

1.6 

0.163 

2 

1.2 

O.I 

4 

0.25 

4 

3-4 

0.15 

6 

0.30 

5 

5.2 

0.2 

8 

0.36 

6 

7 

0.6 

24 

1.  00 

16 

21 

I 

40 

1.96 

26 

32 

i-5 

60 

3.61 

30 

43 

2 

80 

5.76 

35 

48 

3 

120 

11.56 

40 

5i 

5 

200 

29.2 

50 

47 

7 

280 

54-8 

52 

40 

10 

400 

108.2 

34 

27 

12 

480 

154 

27 

18 

'5 

600 

237 

9 

5 

18 

720 

338 

8 

0 

20 

800 

416 

4 

0 

I  (+i  c.c.  aq.) 

40 

5.76 

21 

22 

5  (+i  c.c.  aq.) 

200 

41.0 

48 

35 

10  (+i  c.c.  aq.) 

400 

130 

30 

17 

perhaps  this  difficulty  depends  upon  a  different  solubility 
of  the  precipitate  in  rabbit-serum  and  in  i  per  cent  solu- 
tion of  sodium  chloride.  Perhaps  even  a  difference  of  tem- 
perature in  the  two  parts  of  the  series  is  responsible  for 
the  disagreement;  it  is  really  the  weak  point  of  these 
measurements  that  the  temperature  cannot  be  controlled 
during  the  centrifugation.  But  in  any  case  there  can  be 
no  doubt  that  the  chief  part  of  the  phenomenon  is  repre- 
sented by  the  last  formula. 


THE  PRECIPITINS  AND  THEIR  ANTIBODIES 


295 


ACTION  OF  SERUM  FROM  A  RABBIT,  IMMUNISED  WITH  SHEEP-SERUM, 
ON  BULLOCK-SERUM  (A) 


QUANTITY  OF  A 

V* 

QUANTITY  P  OF  PRECIPITATE 

c.c. 

Equiv. 

obs. 

calc. 

0.02 

0.8 

0.162 

I 

o-5 

0.04 

1.6 

0.163 

2 

i-3 

O.I 

4 

0.25 

4 

3-4 

O.I5 

6 

0.30 

5 

5-2 

0.2 

8 

0.36 

7 

6.7 

0.6 

24 

1.  00 

16 

19 

I 

40 

I.96 

20 

24 

l-J 

60 

3-61 

22 

26 

2 

80 

5.76 

25 

26 

3 

1  20 

II.S6 

28 

25 

5 

200 

29.2 

22 

21 

7 

280 

54-8 

IO 

17 

10 

400 

108.2 

7 

II 

12 

480 

154 

5 

7 

15 

600 

237 

3 

i 

18 

720 

338 

2 

0 

20 

800 

416 

I 

0 

l(+I  c.c.  aq.} 

40 

5.76 

16 

15 

5(+I  c.c.aq.} 

200 

41 

13 

16 

io(+  I  c.c.  aq.} 

400 

130 

5 

7 

This  is  to  a  still  higher  degree  valid  for  the  experiments 
with  bullock-serum,  reproduced  above.  One  c.c.  of  this 
serum  contained  40  equivalents,  0.4  c.c.  of  the  rabbit-serum 
only  35  equivalents.  KWZLS  found  to  be  equal  to  85. 

The  agreement  is  very  satisfying. 

The  conclusions  which  may  be  drawn  from  these  three 
series  are  rather  interesting.  On  injection  of  sheep- 
serum  into  rabbit  blood  we  have  obtained  an  antiserum 
containing  per  centimeter  cube  300  equivalents  of  pre- 


296  LECTURES  ON  IMMUNITY 

cipitin  against  sheep-serum,  212  equivalents  of  precipitin 
against  goat-serum,  and  only  90  equivalents  of  pre- 
cipitin against  bullock-serum.  All  of  these  three  normal 
sera  contain  2000  equivalents  per  centimeter  cube.  In 
the  same  manner  and  in  nearly  the  same  proportion 
the  constant  of  reaction  sinks  from  250  for  sheep-serum 
to  about  170  for  goat-  and  to  85  for  bullock-serum. 
Probably  the  sheep-serum  contains  additional  substances 
which  occur  also  in  sera  of  goats  and  of  bullocks,  which 
after  injection  into  rabbits  produce  antibodies  against 
these  sera,  although  in  lesser  proportions  than  the  pre- 
cipitin against  the  chief  substance  in  sheep-serum,  which 
gives  a  precipitate  with  the  serum  from  the  inoculated 
rabbit.  The  observations  lead  to  the  conclusion  that 
we  have  a  mixture  of  three  different  precipitins  in  the 
rabbit-serum.  Otherwise  it  is  difficult  to  understand  that 
i  c.c.  of  all  the  three  normal  sera,  from  sheep,  goat, 
and  bullock,  contain  nearly  the  same  number  (2000)  of 
equivalents  of  the  precipitate  formed.  As  100  equivalents 
pack  a  volume  of  0.04  c.c.,  the  precipitates  given  by  i  c.c. 
of  the  rabbit-serum  would  pack  a  volume  of  0.24  c.c., 
of  which  probably  only  a  small  part  is  derived  from  this 
serum  itself,  the  chief  part  being  derived  from  the  other 
sera. 

The  experiments  with  precipitins  lead  to  the  conclusion 
that  they  are  really  bound  in  the  precipitates  and  do  not 
act  as  catalytic  agents.  The  action  of  agglutinins  dis- 
plays a  very  great  similarity  to  that  of  the  precipitins,  so 
that  it  is  reasonable  also  for  this  case  to  assume  a  real 
chemical  reaction  in  stoichiometric  proportions  and  not  a 
catalytic  action.  Further,  we  have  observed  that  haemo- 


THE   PRECIPITINS  AND  THEIR  ANTIBODIES  297 

lytic  substances,  such  as  tetanolysin,  are  bound  to  the  sub- 
stance acted  upon,  so  that  a  given  quantity  of  lysin  can 
lake  only  a  given  equivalent  quantity  of  erythrocytes  (cf. 
pp.  104,  in).  Even  for  the  agglutinins  such  an  equivalence 
has  been  observed.  It  is  a  general  feature  of  the  theory  of 
Ehrlich  that  he  assumes  that  the  action  of  poisons  depends 
upon  a  binding,  or  as  he  often  says  an  "anchoring,"  of  the 
poison  to  the  substrate  upon  which  it  acts.  In  this  regard 
Ehrlich  goes  however  a  little  too  far,  since  he,  for  instance, 
supposes  that  all  the  immune-body  absorbed  by  an  ery- 
throcyte  is  "  anchored  "  to  it. 

Furthermore,  we  have  found  that  on  neutralising  a 
poison  or  an  analogous  substance  with  its  antibody,  a  real 
binding  takes  place  according  to  stoichiometrical  propor- 
tions. It  may  here  be  observed  that  in  some  cases  —  and 
these  are  perhaps  rather  common  (cf.  p.  267),  as  for  in- 
stance in  the  coagulation  of  casein — the  reacting  substance 
is  really  not  a  single  one  but  two,  rennet  and  calcium  ions ; 
the  antibody  (e.g.  that  from  normal  horse-serum)  binds 
only  the  one  component  of  the  reacting  mass  (here  the 
calcium  ions),  probably  leaving  the  rennet  intact.  In  simi- 
lar cases  it  is  very  easily  possible  that  the  one  component 
that  is  not  bound  by  the  antibody  acts  as  a  catalysor. 
This  seems  very  probable  for  rennet,  as  the  time  necessary 
for  coagulation  is  within  very  wide  limits  inversely  pro- 
portional to  its  quantity. 

Nevertheless,  on  the  whole,  we  obtain  from  a  closer 
study  of  these  phenomena  the  opinion  that  the  catalytic 
action  does  not  play  the  chief  r61e  which  has  been  often 
assigned  to  it  by  different  authors.  Ehrlich  has  on  re- 
peated occasions  rightly  laid  stress  upon  the  necessity  of  an 


298  LECTURES  ON  IMMUNITY 

investigation  of  the  relations  between  toxins  and  antitoxins 
according  to  the  general  principles  of  physical  chemistry.1 

In  the  foregoing  pages  I  have  tried  to  carry  through  the 
programme  advocated  so  strongly  by  Ehrlich.  That  this 
has  been  possible,  is  due  in  large  part  to  the  great  num- 
ber of  quantitative  measurements  which  have  been  carried 
out  in  the  last  quinquennium,  especially  by  Madsen  and 
his  collaborators.  This  work  is  still  in  full  progress ;  and 
it  may  therefore  be  well  regarded  as  very  probable  that 
we  are  here  entitled  to  use  the  words  with  which  Dr.  Find- 
lay  2  closed  his  lectures  in  the  University  of  Birmingham, 
"  Considering  the  very  brief  period  during  which  physical 
chemical  methods  have  found  application  to  the  study  of 
biological  problems,  the  advance  which  has  been  made  is 
very  remarkable ;  and  there  is  every  reason  to  believe  that 
in  the  future,  as  the  methods  become  more  and  more 
extensively  applied,  the  advance  will  become  more  rapid 
and  widespread."  Our  hope  in  this  direction  lies  chiefly 
in  the  treatment  of  quantitative  experiments  on  the  basis 
of  physical  chemistry.  It  may  be  confidently  expected 
that  the  accumulating  quantitative  work  will  rapidly  give 
solidity  to  this  discipline  of  science.  I  know  well  that 
objections  have  been  raised  to  some  of  the  conclusions 
that  I  have  here  enunciated.  But  it  is  clear  to  me  that,  if 
these  objections  are  to  deserve  a  more  than  momentary 

1  Cf.  P.  Ehrlich :  Rapport  au  13*  Congrh  Internationale  de  medicine,  Paris, 
2-9  Aoftt,  1900,  Section  de  bacteriologie ;  "  Schlussbetrachtungen,"  "Nothna- 
gel's  spezielle  Pathologic  und  Therapie,"  T.  8,  pp.  6-7,  Wien,  1901 ;  Bericht 
iiber  die   Th'dtigkeit  des  Instituts  f.  Serumforschungen  zu  Sieglitz,  p.  19,  Jena, 
1899  (G.  Fischer)  ;    "UeberToxine  und  Antitoxine"  in  Therapie  der  Gegen- 
wart,  1901. 

2  Al.  Findlay :  "  Physical  Chemistry  and  its  Applications  in  Medical  and 
Biological  Science,"  p.  68,  Longmans,  Green  &  Co.,  London,  1905. 


THE   PRECIPITINS  AND  THEIR  ANTIBODIES  299 

interest,  they  must  be  shown  to  agree  with  the  quantitative 
measurements  already  executed  or  with  other  new  ones. 

In  the  foregoing  discussions  it  has  been  shown  that  the 
available  observations  conform  to  the  laws  deduced  by 
physical  chemistry  for  common  chemical  compounds. 
Therefore  discussions  as  to  whether  toxins  and  their 
antitoxins,  being  defined  as  colloids,  might  be  held  not 
subject  to  these  general  chemical  laws,  will  possess  but 
little  interest  until  the  assumed  deviations  from  said 
laws  are  measured  quantitatively.  Any  other  method  of 
procedure  has  a  very  hypothetical  value. 


INDEX   OF   AUTHORS 


Aberson,  139,  140. 

Armstrong,  55,  57,  58,  61,  134. 

Arrhenius,  i,  13,  15,  25,  29,  45,  62, 
68,  100,  no,  150,  167,  180,  181,  189, 
190,  200,  224,  231-239,  250,  261,  288. 

B 

Bang,  71,  267. 

Barendrecht,  52. 

Bashford,  i,  205,  206,  245,  252,  272, 

273- 

Bayliss,  79,  136,  163. 
Bechhold,  156-160,  166,  282. 
Behring,  29,  152,  179. 
Besredka,  i. 
Biernacki,  277. 
Biltz,  35,  151,  152,  155,  156,  165,  215, 

216,  217,  231,  278. 
Blum,  266. 
Bodenstein,  54,  60. 
Bomstein,  5,  7. 
Bordet,  20,  21,  32,  34,  151,  218,  219, 

223,    225,    242,    246,    247,    252-260, 

270,  271,  281. 
Borissow,  121,  122. 
Bossaert,  166. 
Bredig,  50,  152,  161. 
Brodie,  28. 
Brown,  52,  55,  58. 
Bruck,  24. 
Buchner,  30,  141,  218. 


Calcar,  200. 
Calmette,  18,  19,  30. 
Cherry,  18,  26,  30. 
Clausen,  136. 
Cohen,  136. 
Connstein,  125,  132. 
Craw,  26-28. 


Danysz,  22,  190,  192,  194. 

Detre,  241,  242. 

Dreyer,  31,  151,  198. 

Duclaux,  52,  57,   164,   194,  263,  268, 

269. 
v.  Dungern,  2,  190,  194,  228. 


Ehrlich,  9,  11-15,  r9-2I»  3°.  31.  152, 
177,  180,  182-185,  X89,  197,  205,  219, 
223,  225-227,  231,  246,  247,  256- 
261,  272,  273,  277,  278,  282,  297, 
298. 

Eisenberg,  17,  32,  34,  116,  I44~i47» 
281,  283-285. 

Emmerling,  133,  134. 

Engel,  124,  135. 

Euler,  50,  51,  84,  141,  142. 


Famulener,  21,  39,  40,  42,  47. 

Findlay,  298. 

Fischer,  134. 

Fischer,  E.,  134,  161. 

Ford,  256. 

Freundlich,  161. 

Friedberger,  246,  282. 

Fuld,  73,  76,  97,  185,  278,  280. 


Gay,  252,  254,  255,  260. 

Gengou,  270,  271. 

Gessard,  2. 

Girard-Mangin,  163,  164. 

Glendinning,  55. 

Godlewski,  136. 

Goldschmidt,  142. 

Gruber,  220,  228,  231. 

Guldberg,  i,  28,  133,  175,  216,  279. 


301 


302 


INDEX  OF  AUTHORS 


H 

Hamburger,  287-296. 

Hammarsten,  3,  71,  266-268,  270,  276 

Hanriot,  126,  134. 

Hausmann,  272. 

Hedin,  266. 

Hemmeter,  71,  267. 

Henderson  Smith,  103. 

Henri,  51-56,  59,  60,  80-84,  Jo5>  IQ6, 

139,  156,  163,  164. 
Hertwig,  138. 
Herzog,  141. 
Hildebrand,  2. 
Hill,  133. 
Hober,  10,  222. 
van  't  Hoff,  28,  35,  98,  136. 
Hoyer,  125,  132. 
Huppert,  69,  70. 


Jacoby,  272. 
Joos,  34,  146,  153. 
Jorgensen,  4,  6,  15,  17,  91. 


Kanitz,  137. 

Kastle,  126,  132,  134. 

Kitasato,  29. 

Kjeldahl,  53,  98. 

Klein,  254. 

Kobert,  273. 

Kossel,  12,  161. 

Kraus,  164,  165,  272. 

Kyes,  10,  190,  209-214,  240. 


Lalou,  84. 

Landois,  218. 

Landsteiner,  32. 

Laqueur,  266. 

Larguier  de  Bancels,  80-83. 

Loeb,  J.,  138,  139,  161,  164. 

Loeb,  L.,  271. 

Loercher,  265. 

Loewenhart,  126,  132,  134. 

Ludwig,  272. 

Lunden,  176. 

M 

Madsen,  i,  4,  5,  6,  7,  10,  13,  15,  17,  21- 
23.  25,  29,  31,  33,  39,  40,  42-44,  46, 
47.  70.  72,  77.  78,  86,  88-100,  103, 


107-117,  135,  154,  167,  180,  181, 
186-190,  196-198,  200,  202,  203,  204, 
206-213,  274»  298. 

Malkoff,  149. 

Malloizel,  163. 

Manwaring,  229. 

Marshall,  189. 

Martin,  18,  26,  30. 

Matthaei,  137. 

Metchnikoff,  231. 

Mett,  121. 

Meyer,  H.,  24. 

Morgenroth,  i,  2,  20,  31,  32,  34,  35,  76, 
150,  189,  199,  214,  215,  219-221,  228, 
229,  231,  244-251,  256,  257,  259,  262, 
268,  274. 

Much,  35,  151,  152. 

Miiller,  P.  T.,  22,  189,  281-283. 

Miiller  von  Berneck,  50. 

Musculus,  134. 

Myers,  273. 

N 

Neisser,  21,  189,  224-227. 

Nernst,  28,  35,  148,  152. 

Nicloux,  97,  98,  128,  129. 

Nicolle,  164,  165. 

Noguchi,  23,  107,  109,  in,  206-213. 


Ostwald,  68,  133, 184. 
O'Sullivan,  58. 
Overton,  10,  222. 


Pasteur,  141. 

Pauli,  160,  161,  162,  164. 

Pawlow,  71,  77,  122,  267. 

Peter,  138. 

Pfeififer,  246. 

Pick,  284. 

Portier,  194. 

R 

Ransom,  10,  24,  147,  220. 
Reichel,  73. 
Reid,  25. 
Richet,  194. 
Ritchie,  45,  46. 
Robertson,  134. 


INDEX  OF  AUTHORS 


303 


Rdde"n,  3,  276. 
Romer,  200. 
Roux,  30. 

S 

Sachs,  2,  10,  29,  35,  190,  211,  214,  218, 
222,  223,  228,  231,  241,  242,  244,  245, 
248-251,  257-262. 

Sackur,  266. 

Sawjalow,  71,  76,  77,  119,  121,  267. 

Schmidt,  A.,  270. 

Schmidt,  G.,  151,  216. 

Schmidt-Nielsen,  71,  267. 

Schiitz,  Emil,  62,  67,  69,  70,  119. 

Schlitz,  Julius,  67. 

Schiitze,  2,  3,  287. 

Segelcke,  71. 

Sellei,  241,  242. 

Siebert,  35,  151,  152. 

Siedentopf,  264. 

Sjoqvist,  65-69,  119-121,  123,  162,  163. 

Snyder,  139. 

Soxhlet,  71. 

Spiro,  73,  185,  278,  280. 

Spohr,  98. 

Stade,  123-125,  135. 

Storch,  71. 


Tammann,  48,  49,  59,  97,  98,  126. 
Taylor,  A.  E.,  83,  98,  126,  130-133,  134. 


Terroine,  54,  55,  59,  61. 
Tompson,  58. 
Tyndall,  264. 


U 


Uhlenhuth,  287. 


Vaubel,  266. 

Volhard,  122,  135. 

Volk,  17,  32,  116,  144-147,  284. 

W 

Waage,  i,  28,  133,  175,  216,  279. 

Walbum,  10,  21,  23,  33,  77,  78,  86,  89, 
90,  92-97,  107,  109,  in,  113,  ii4t 
135,  154,  186,  188,  200,  203,  204, 
274. 

Warder,  98. 

Wartenberg,  125,  132. 

Wassermann,  12,  19,  24,  256,  287. 

Wechsberg,  21,  189,  224-227. 

Weigert,  n,  257. 

Weis,  84. 

Wohl,  134. 


Zeller,  128. 


INDEX   OF   MATTER 


Abrin,  2,  272. 

Absorption,  32,  33,  144-155,  207,  216, 
219,  297. 

Acetic  acid,  166,  283. 

Acids,  coagulating  action,  266,  270, 
272;  destroying  action,  35,  43,  44, 
45,  138;  digesting  action,  69,  126; 
haemolytic  action,  in,  167, 171;  neu- 
tralisation, 35,  222. 

Active  immunisation,  6,  218. 

Acme,  4. 

Adrenalin,  24. 

Adsorption,  32,  35,  151,  152,  215,  216. 

Agglutination,  agglutinins,  4,  9,  14,  17, 
32,  115,  116,  144-166,  219,  241,  256, 
284,  287. 

Agglutinoid,  155. 

Albumen,  65,  92,  119,  189. 

Albumen  precipitin,  273,  281,  285,  286. 

Albumose,  retarding  influence  of,  77; 
equivalent  weight,  162. 

Alcoholic  fermentation,  139-142. 

Alexin,  20,  34,  48,  218-262. 

Alkali,  haemolysis  through,  in,  167- 
177;  influence  on  eggs,  138;  on 
toxicity,  222;  on  coagulation,  266. 

Alkaloids,  toxicity,  222. 

Alopecia,  198. 

Amanita  muscaria,  128. 

Amboceptor,  cf.  Immune-bodies. 

Ammonia,  destroying  action,  42; 
haemolytic  action,  101-103,  I7It  J72J 
saponification,  62-65. 

Amphoteric  electrolytes,  161-163. 

Amygdalin,  59,  84. 

Ancistrodon,  see  Water-moccasin. 

Antialexin,  246-252,  261,  262. 

Anti-antitoxin,  245. 

Antibodies,  formation  and  decomposi- 
tion, i,  3-7,  179,  257-259;  in  normal 
serum,  3,  9,  165,  185,  274-277. 


Antihaemolysin,  247,  262. 
Anti-immune-body,  246-252,  261,  262. 
Antimorphine,   i. 
Anti-sensibilisator,  246. 
Antitoxins,  9;   decomposition,  4-9,  46; 

standardisation,     14;      cf.     corresp. 

Toxins. 

Antivenin,   18,  209-214. 
Arachnolysin,    10,    214;     ascites-fluid, 

276;   asparagin,  80. 
Assimilation,  137. 
Attenuation,  influence  of,  49,  88,  loa- 

104,  169,  170,  191,  229,  230. 

B 

Bacillus  botulinus,  154. 

Bacillus  coli,  86,  104,  151,  165,  166. 

Bacillus  megatherium,  27. 

Bacillus  pyocyaneus,  19,  86,  182. 

Bacillus  tetani,  10,  24. 

Bacteriolysins,  9,  17,  21,  224. 

Barium  salts,  265,  270. 

Bimolecular  reactions,  38,  87,  93,  136. 

Blood-plasma,  269-271. 

Boletus  scaber,  50. 

Boracic  acid,  171,  175. 

Botulismus-poison,  154,  241. 

Brownian  movement,  263. 


Calcium  salts,  influence  of,  74,  185,  265, 
268,  269,  270,  279,  282,  297;  of 
casein,  266;  of  para-casein,  266,  279. 

Cane-sugar,  inversion  of,  38,  51-54, 
57-58,  98.  _ 

Carbonic  acid,  assimilation  of,  137; 
respiration  of,  136. 

Casein,  79,  81,  135,  262;  coagulation, 
72-76,  297;  precipitation,  22,  281- 
283. 

Castor  beans,  see  Ricinus  seeds. 


305 


306 


INDEX   OF   MATTER 


Catalase,  50,  51. 

Catalysis,  catalysator,  30,  57,  133,  223, 

235,  296,  297. 
Chlorophyll,  137. 
Cholera- agglutinin,  3. 
Cholera-precipitin,  284. 
Cholera  vibrions,  3,  144,  164,  165. 
Cholesterin,  9,  10,  n,  23,  147,  155,  187, 

189,  206,  214,  220,  242. 
Chymosin,  267,  274. 
Coagulation,  17,  71,  164-166. 
Cobra-lecithid,  10,  213,  214,  238-240. 
Cobra-poison,    10,   34,    117,    190,   210, 

212,  242,  274. 
Coelenterates,  194. 
Coli- agglutinin,  86,  91,  115,  151. 
Colloide  de  boeuf,  260. 
Colloids,  28,  35,  151-153,  156,  163,  215, 

216,  263;  retarding  influence,  159. 
Colorimetric  methods,  15.  , 

Complement,  see  Alexin. 
Crotalus-poison,  202,  209,  212. 
Crotin,  272,  273. 
Cyclamin,  274. 
Cynarase,  3. 

D 

Diastase,  51,  55. 

Dibrom-succinic  acid, 

Diffusion  of  enzymes,  toxins,  and  anti- 
toxins, 24-28,  33,  121,  132,  134,  142, 
i53»  227. 

Digestion,   61,   65-69,  77-86,  89,  119, 

135- 

Digitalin,  274. 

Diphtheria-antitoxin,  5,  245. 
Diphtheria- poison,  11-14,  18,   26,   152, 

177,  190,  196-202. 
Diversion  of  alexin,  224-228,  244. 
Dog's  serum,  105. 


Eggs,  influence  of  temperature  on  de- 
velopment of,  138. 

Egg-white,  3,  61,  69,  79,  160,  162. 

Ehrlich's  phenomenon,  177-185,  187. 

Electric  charges,  117,  156,  160,  163. 

Emulsin,  2,  48,  49,  55,  57,  59,  84. 

Enzymes,  2,  3,  48,  57-60,  142;  com- 
pounds of,  57,  60-62. 

Epitoxin,  177,  197-200. 


Equilibria,  31,  118,  125,  126,  132-134, 

IS5i  l(>9,  180-182,  184,  202,  205,  215, 

217,  231-251,  288-293. 
Equivalency,  in,  170,    171,    172,    188, 

254,  288-293. 
Equivalent  weights  of  albumose,  162; 

casein,  266;  pepton,  162;  egg-white, 

162. 

Ethyl-butyrate,  51. 
Euglobulin,  279. 


Fats,  saponification  of,  51,  61,  119, 126- 

134- 

Ferments,  2,  3 ;  see  also  Enzymes. 
Fibrine,  270. 

Fibrin-ferment,  3,  91,  269,  271. 
Filtration,  26,  27,  164,  268. 
Fluorides,  269,  271. 
Formalin,  166,  283,  287. 
Formulae,  use  of,  7. 


Gelatine,  70,  77,  78,  81,  82,  86. 

Globuline,  273. 

Glucose,  53,  133,  139-142. 

Glycin,  80,  84. 

Goat's  serum,  47,  220,   221,  228,  233, 

243,  246,  247,  249,  250,  256,  261,  274, 

291,  294,  296. 
Goose,  extract  of  muscles,  92;   plasma 

of,  92,  280;  serum  of,  2. 
Guinea-pig,  normal,  12;   serum  of,  19, 

224,  228,  233,  236,  237,  238,  244,  245, 

246,  249,  250,  253,  256,  260,  261. 

H 

Haemolysis,  haemolysins,  9,  15,  16,  47, 
105,  117,  167,  189,  206-211,  274; 
compound,  218-262. 

Haptophor,  183. 

Heart-beats  (influence  of  temperature), 

139- 

Hen's  serum,  256. 
Hirudin,  280. 
Horse-serum,  3,  9,  165,  189,  208,  222, 

254,  255,  260,  274-278,  287;  plasma, 

92. 

Hydrochloric  acid,  35,  43. 
Hydrogen  peroxide,  50,  166. 


INDEX   OF  MATTER 


307 


Hydrolysis,  171,  174,  222,  283. 
Hypnotoxin,  195. 


Immune-bodies,  3,  19,  20,  48,  150,  219- 

261. 

Immune-serum,  3,  219-261. 
Immunisation,  6,  219-261. 
Inactivation,  19. 
Incomplete  reactions,  29,  30. 
Injection,  i,  2,  7-8;   of  cells,  2. 
Intra-cardial,     -muscular,     -peritoneal, 

-venous  injection,  7-8. 
Inversion  of  cane-sugar,  38,  51-54,  57, 

58,  59- 

Invertin,  51-55,  58. 
"In  vitro"  and  "in  vivo"  reactions,  14, 

15,  16,  30,  205,  273,  274. 
Isocasein,  266. 


Lactase,  2,  55,  57,  58. 

Lactoserum,  22,  281-286. 

Lecithin,  9,  10,  210,  238-242. 

Leeches,  280. 

Lethal  dose,  12,  13,  154,  198. 

Leucin,  80. 

Leucocytes,  269. 

Lipase,  65,  119. 

Lipolysis,  see  Fats. 

Lysins,  9. 

M 

Magnesium-salts,  265. 

Malt,  extract  of,  84. 

Maltase,  53-55,  59. 

Maltose,  53-55,  59,  133. 

Mass  action,  i,  28,  133,  175,  216,  245, 

279. 

Mastic  emulsion,  157-159. 
Mercuric  chloride,  115,  166,  273. 
Mett's  tubes,  121,  142. 
Migration  in  electric  field,  160-162. 
Milk,  21 ;  coagulation  of,  71-76. 
Milk-sugar,  56,  57,  58. 
Molecular- weight  of  casein,  266;  toxins 

and  antitoxins,  25;   haemoglobin,  26. 
Monomolecular  reactions,   37,   52,   68, 

87,  89,  101-106,  120,  130,  191. 
Morphin,  i. 


Muscles,  extract  of,  92,  280. 
Mushroom,  2,  128. 

N 

Naja,  see  Cobra. 
Neutralisation,  29,   161-163,   167-181, 

234-239. 
Neutralised  poison,  14,  21-28,  30,  34, 

152,  167-181,  192-217. 
w-molecular  reaction,  38,  95. 


Oleate  of  sodium,  114,  142. 

Oleic  acid,  113,  167. 

Olein,  derivatives  of, 

Olive  oil,  10. 

Optimum,  70,   73,   117,   129,   137-139, 

^S-iSS,  241,  285. 
Oxalates,  269-272,  282. 
Ox-serum,  208,  218,  222,  254,  260,  276, 

287,  291,  295,  296. 


Pancreatic  ferment,  3,  124. 

Pancreatic  extract,  77,  80. 

Papayotin,  77. 

Para-casein,  268,  283. 

Paresis,  198,  199. 

Partial  toxins,  177,  183. 

Passive  immunisation,  6,  245. 

Pectase,  272. 

Pectin,  271. 

Pepsin,  2,  61,  71,  89,  119,  134,  163,  267. 

Pepton,  77,  80,  93,  162,  273. 

Permeability  of  membranes,    10,    221, 

222,  241,  242,  243,  268. 
Physiological  solution,  8,  15,  172,  254. 
Plague-bacilli,  164. 
Plasma,  91,  269-271. 
Plurality  of  poisons,  177,  183;  of  alexins 

and  antialexins,  252. 
Poisons,  calibration  of,  11-17. 
Potassium  hydrate,   hsemolytic  action, 

170. 
Precipitins,  9,  14,  17,  92,  156,  166,  263- 

299. 

Probable  error,  14,  196,  215,  275. 
Protamin,  83. 
Protein,  84,  164,  189. 
Proteolytic  ferment,  2,  22. 


308 


INDEX  OF  MATTER 


Prototoxoid,  197,  200-204. 
Pseudo-globulin,  279. 
Pseudo-solution,  263,  265,  267. 


Rabbit's  serum,  206,  224,  228,  238,  244, 

246,  247,  249,  253,  254,  255,  258,  273, 

276,  291-296. 
Reaction,  velocity  of,   18,  32,  36-143, 

155,  189,  242,  252,  284. 
Receptor,  257. 
Rennet,  2,  3,  71-76,  87,  88,  185,  190, 

265-269,  270,  275,  283,  297. 
Respiration  of  plants,  136. 
Reversibility  of  reactions,  18-36. 
Ricin,  2,  15,  22,  23,  24,  115,  149,  190, 

203,  272. 

Ricinus  oil,  125-127. 
Ricinus  seeds,  2,  98,  125-127. 
Robin,  2. 


Safranin,  166. 

Salicin,  48,  54,  84. 

Salts,  action  of ,  at  agglutination,  9,  153, 

156-159,  254;  at  haemolysis,  172,  188, 

255;    at  coagulation,  265,  266,  279, 

282. 
Saponification  of  ethyl-acetate,  62-65, 

98;  see  also  Fats. 
Saponin,  i,  10,  n,  23,  147,  169,  206- 

208,  220,  241,  274. 
Schutz'  rule,  62-68,  81,  85,  121-126. 
Sensibilitator,  sensibilisation,   20,   223, 

228,  242. 
Sero-bacilli,  157. 

Serum,  inactivated,  19,  218,  247;   nor- 
mal, 3,  9,  160,  165,  189,  208,  218,  221, 

254,  270,  278,  284. 
Serum-albumen,  268,  283,  285. 
Serum-precipitin,  273,  287-299. 
Sheep's  serum,  228,  237,  291,  292,  294, 

296. 
Side-chain  theory,  31,  177,  180,  182- 

185,  257,  258. 

Snake-poisons,  18,  209-215. 
Sodium  hydrate,  hsemolytic  action,  102; 

action  on  poisons,  41,  44,  88. 
Solanin,  i,  170,  274. 
Solubility,  132. 


Specificity  of  agglutinins,  163;  of  anti- 
toxins, 3,  163,  281. 

Standard  serum,  14. 

Staphylolysin,  10,  21,  107,  187,  189, 
190. 

Starch,  55. 

Statistical  methods,  13. 

Steapsin,  122-125. 

Stomachal  extract,  122;  juice,  77,  122, 
123. 

Strengthening  of  binding,  192. 

Streptococcus,  165,  271. 

Streptolysin,  113,  186,  187. 

Strontium  salts,  265,  270. 

Subcutaneous  injection,  8. 

Sublimate,  see  Mercuric  chloride. 

Sub-microscopic  granules,  264. 

Sulphuric  acid,  92. 

Swine-serum,  276. 

Synthesis,  133. 

Syntoxoid,  202. 


Taurocholate,  170. 

Temperature,  influence,  10,  18,  21,  35, 

40-42,  46-49.  53,  69,  71,  73,  76,  87, 

89,  90,  91,  96-99,  107-117,  180,  268, 

277,  283,  284. 
Terrapin,  Pacific,  139. 
Tetanolysin,  3,  9,  18,  33,  41,  44,  45,  93, 

102-104,  113,  149,  155,  178-182,  187, 

189,  190,  245,  273. 
Tetanospasmin,  24,  152. 
Tetanus  bacilli,  24. 
Thymolgelatine,  70,  77,  78,  86,  89. 
Time  of  reaction,  18,  31,  101,  118,  157, 

Toxicity,  estimation  of,  11-17,  175. 

Toxins,  i. 

Toxoid,  182,  211. 

Toxon,  197-200,  211. 

Toxophor,  183. 

Transfusion,  218. 

Triacetin,  130,  131. 

Triolein,  114,  131,  132. 

Trypsin,  3,  61,  77,  78-81,  86,  89,  90,  91, 

134,  135,  163. 
Typhoid  agglutinin,  5,   115,  144,   151, 

163. 

Typhoid  bacilli,  144,  156,  163-166. 
Typhoid-precipitin,  284. 
Tyrosinase,  2. 


INDEX  OF   MATTER 


309 


Urea,  283,  287. 
Urease,  3. 


Vesuvin,  166. 

Vibrio  cholerae,  see  Cholera  vibrions. 
Vibrio  Metschnikovi,  165. 
Vibriolysin,  39,  40,  41-43,  113,  187. 
Vital  processes,  136. 


W 

Water-moccasin,  117,  211,  213. 
Whey,  75. 


Yeast,  139-141. 
Yolk,  123. 


Zymase,  3,  141. 


The  Common 
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A  History  of  Chemistry 

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